references - springer978-3-642-77625-0/1.pdf · 1.6 m.w. hirsch, s. smale: differential equations,...

12
References Chapter 1 1.1 J. Peinke, J. Parisi, B. Rohricht, O.E. Rossler, W. Metzler: Z. Naturforsch. 43a, 287 (1988) 1.2 Anaxagoras: On Nature (in Greek), Fragment 12, reprinted and translated in G.S. Kirk, J.E. Raven: The Presocratic Philosophers. A Critical History with a Selection of Texts (Cambridge University Press, London 1957) p. 372 1.3 O.E. Rossler: Z. Naturforsch. 38a, 788 (1983) 1.4 S. Smale: Bull. Ani. Math. Soc. 73, 747 (1967) 1.5 O.E. Rossler: Phys. Lett. 57 A, 397 (1976) 1.6 M.W. Hirsch, S. Smale: Differential Equations, Dynamical Systems, and Linear Algebra (Academic, New York 1974) 1.7 O.E. Rossler: In Structural Stability in Physics, ed. by W. Giittinger, H. Eikemeier, Springer Ser. Syn., Vol. 4 (Springer, Berlin, Heidelberg 1979) p. 290 1.8 M. Henon: Commun. Math. Phys. 50, 69 (1976) 1.9 I. Gumowski, C. Mira: Dynamique Chaotique, Transformations Ponctuelles, Transition Ordre Desordre (Cepadues, Toulouse 1980) 1.10 O.E. Rossler: Ann. N.Y. Acad. Sci. 316, 379 (1979); in Iteration Theory and Functional Equations, Lect. Notes Math., Vol. 1163, ed. by R. Liedl, L. Reich, G. Targonski (Springer, Berlin, Heidelberg 1985) p. 149 1.11 O.E. Rossler: Z. Naturforsch. 31a, 1664 (1976) Chapter 2 2.1 I.L. Ivanov, S.M. Ryvkin: Sov. Phys. - Tech. Phys. 3, 722 (1958) 2.2 R.D. Larrabee, M.C. Steele: J. Appl. Phys. 31, 1519 (1960) 2.3 Proc. 5th Int'l Conf. on Semiconductor Physics, Prague, 1960 (Academic, New York 1961); Proc. 7th Int'l Conf. on the Physics of Semiconductors, Paris, 1964 (Academic, New York 1965); Proc. 9th Int'l Conf. on the Physics of Semiconductors, Moscow, 1968 (Nauka, Leningrad 1968) 2.4 V.L. Bonch-Bruevich, I.P. Zvyagin, A.G. Mironov: Domain Electrical Instabilities in Semi conductors (Consultants Bureau, New York 1975) 2.5 J. Pozhela: Plasma and Current Instabilities in Semiconductors (Pergamon, Oxford 1981) 2.6 E. SchoU: Nonequilibrium Phase Transitions in Semiconductors, Springer Ser. Syn., Vol. 35 (Springer, Berlin, Heidelberg 1987) 2.7 B.K. Ridley: Proc. Phys. Soc. 82, 954 (1963) 2.8 J. Peinke, D.B. Schmid, B. Rohricht, J. Parisi: Z. Phys. B 66, 65 (1987) 2.9 K.M. Mayer, J. Peinke, B. Rohricht, J. Parisi, R.P. Huebener: Phys. Scr. T19, 505 (1987) 2.10 M.A. Lampert, R.B. Schilling: In Semiconductors and Semimetals, Vol. 6, ed. by R.K. Willardson, A.C. Beer (Academic, New York 1970) p. 1 2.11 A.A. Kastalsky: Phys. Status Solidi (a) 15, 599 (1973) 2.12 M. Glicksman: In Solid State Physics, Vol. 26, ed. by H. Ehrenreich, F. Seitz, D. TurnbuU (Academic, New York 1971) p. 275

Upload: trinhtu

Post on 15-Aug-2018

219 views

Category:

Documents


0 download

TRANSCRIPT

References

Chapter 1

1.1 J. Peinke, J. Parisi, B. Rohricht, O.E. Rossler, W. Metzler: Z. Naturforsch. 43a, 287 (1988) 1.2 Anaxagoras: On Nature (in Greek), Fragment 12, reprinted and translated in G.S. Kirk,

J.E. Raven: The Presocratic Philosophers. A Critical History with a Selection of Texts (Cambridge University Press, London 1957) p. 372

1.3 O.E. Rossler: Z. Naturforsch. 38a, 788 (1983) 1.4 S. Smale: Bull. Ani. Math. Soc. 73, 747 (1967) 1.5 O.E. Rossler: Phys. Lett. 57 A, 397 (1976) 1.6 M.W. Hirsch, S. Smale: Differential Equations, Dynamical Systems, and Linear Algebra

(Academic, New York 1974) 1.7 O.E. Rossler: In Structural Stability in Physics, ed. by W. Giittinger, H. Eikemeier, Springer Ser.

Syn., Vol. 4 (Springer, Berlin, Heidelberg 1979) p. 290 1.8 M. Henon: Commun. Math. Phys. 50, 69 (1976) 1.9 I. Gumowski, C. Mira: Dynamique Chaotique, Transformations Ponctuelles, Transition Ordre­

Desordre (Cepadues, Toulouse 1980) 1.10 O.E. Rossler: Ann. N.Y. Acad. Sci. 316, 379 (1979); in Iteration Theory and Functional

Equations, Lect. Notes Math., Vol. 1163, ed. by R. Liedl, L. Reich, G. Targonski (Springer, Berlin, Heidelberg 1985) p. 149

1.11 O.E. Rossler: Z. Naturforsch. 31a, 1664 (1976)

Chapter 2

2.1 I.L. Ivanov, S.M. Ryvkin: Sov. Phys. - Tech. Phys. 3, 722 (1958) 2.2 R.D. Larrabee, M.C. Steele: J. Appl. Phys. 31, 1519 (1960) 2.3 Proc. 5th Int'l Conf. on Semiconductor Physics, Prague, 1960 (Academic, New York 1961);

Proc. 7th Int'l Conf. on the Physics of Semiconductors, Paris, 1964 (Academic, New York 1965); Proc. 9th Int'l Conf. on the Physics of Semiconductors, Moscow, 1968 (Nauka, Leningrad 1968)

2.4 V.L. Bonch-Bruevich, I.P. Zvyagin, A.G. Mironov: Domain Electrical Instabilities in Semi­conductors (Consultants Bureau, New York 1975)

2.5 J. Pozhela: Plasma and Current Instabilities in Semiconductors (Pergamon, Oxford 1981) 2.6 E. SchoU: Nonequilibrium Phase Transitions in Semiconductors, Springer Ser. Syn., Vol. 35

(Springer, Berlin, Heidelberg 1987) 2.7 B.K. Ridley: Proc. Phys. Soc. 82, 954 (1963) 2.8 J. Peinke, D.B. Schmid, B. Rohricht, J. Parisi: Z. Phys. B 66, 65 (1987) 2.9 K.M. Mayer, J. Peinke, B. Rohricht, J. Parisi, R.P. Huebener: Phys. Scr. T19, 505 (1987) 2.10 M.A. Lampert, R.B. Schilling: In Semiconductors and Semimetals, Vol. 6, ed. by R.K.

Willardson, A.C. Beer (Academic, New York 1970) p. 1 2.11 A.A. Kastalsky: Phys. Status Solidi (a) 15, 599 (1973) 2.12 M. Glicksman: In Solid State Physics, Vol. 26, ed. by H. Ehrenreich, F. Seitz, D. TurnbuU

(Academic, New York 1971) p. 275

278 References

2.13 K. Yamada, N. Takara, H. Imada, N. Miura, C. Hamaguchi: Solid-State Electron. 31, 809 (1988); K. Yamada, N. Miura, C. Hamaguchi: App!. Phys. A 48, 149 (1989)

2.14 D.G. Seiler, C.L Littler, RJ. Justice, P.W. Milonni: Phys. Lett. 108A, 462 (1985); X.N. Song, D.G. Seiler, M.R Loloee: App!. Phys. A 48, 137 (1989)

2.15 K. Aoki, T. Kobayashi, K. Yamamoto: J. de Phys. 42, C7-51 (1981); J. Phys. Soc. Jpn. 51, 2373 (1982); K. Aoki, K. Yamamoto: Phys. Lett. 98A, 72 (1983); K. Aoki, K. Miyamas, T. Kobayashi, K. Yamamoto: Physica 117/118 B + C, 570 (1983); K. Aoki, O. Ikezawa, N. Mugibayashi, K. Yamamoto: Physica 134B, 288 (1985); K. Aoki, K. Yamamoto, N. Mugibayashi: J. Phys. Soc. Jpn. 57, 26 (1988); K. Aoki, K. Yamamoto: App!. Phys. A 48, 111 (1989)

2.16 A. Brandl, T. Geisel, W. Pretti: Europhys. Lett. 3, 401 (1987); J. Spangler, A. Brandl, W. Pretti: App!. Phys. A 48, 143 (1989); U. Frank, A. Brandl, W. Pretti: Solid State Commun. 69, 891 (1989)

2.17 S.W. Teitsworth, RM. Westervelt, E.E. Haller: Phys. Rev. Lett. 51, 825 (1983); S.W. Teitsworth, RM. Westervelt: Phys. Rev. Lett. 56, 516 (1986); E.G. Gwinn, RM. Westervelt: Phys. Rev. Lett. 57, 1060 (1986); ibid. 59, 157, 247 (1987); S.W. Teitsworth: App!. Phys. A 48, 127 (1989)

2.18 J. Peinke, A. Miihlbach, R.P. Huebener, J. Parisi: Phys. Lett. 108A, 407 (1985); J. Peinke, B. Rohricht, A. Miihlbach, J. Parisi, Ch. Noldeke, R.P. Huebener, O.E. Rossler: Z. Naturforsch. 408, 562 (1985); J. Peinke, J. Parisi, B. Rohricht, B. Wessely, K.M. Mayer: Z. Naturforsch. 428, 841 (1987); U. Rau, J. Peinke, J. Parisi, R.P. Huebener, E. Scholl: Phys. Lett. 124A, 335 (1987); R Stoop, J. Peinke, J. Parisi, B. Rohricht, RP. Huebener: Physica 35D, 425 (1989); J. Parisi, J. Peinke, R.P. Huebener, R Stoop, M. Duong-van: Z. Naturforsch. 448, 1046 (1989); J. Peinke, J. Parisi, RP. Huebener, M. Duong-van, P. Keller: Europhys. Lett. 12, 13 (1990)

2.19 J. Spinnewyn, H. Strauven, O.B. Verbeke: Z. Phys. B 75, 159 (1989) 2.20 K.A. Pyragas, J. Pozhela, A.V. Tamasevicius, J.K. Ulbikas: SOY. Phys. - Semicond. 21, 335

(1987); J. Pozhela, A.V. Tamasevicius, J.K. Ulbikas: Solid-State Electron. 31, 805 (1988); J. Pozhela, A. Namajunas, A.V. Tamasevicius, J.K. Ulbikas: App!. Phys. A 48, 181 (1989)

2.21 G.N. Maracas, W. Porod, D.A. Johnson, D.K. Ferry, H. Goronkin: Physica 134B, 276 (1985); G.N. Maracas, D.A. Johnson, H. Goronkin: App!. Phys. Lett. 46, 305 (1985)

2.22 W. Knap, M. Jezewski, J. Lusakowski, W. Kuszko: Solid-State Electron. 31, 813 (1988) 2.23 G.A. Held, C. Jeffries, E.E. Haller: Phys. Rev. Lett. 52, 1037 (1984);

G.A. Held, C. Jeffries: Phys. Rev. Lett. 55, 887 (1985); ibid. 56, 1183 (1986) 2.24 S.B. Bumeliene, J. Pozhela, K.A. Pyragas, A.V. Tamasevicius: Physica 134B, 293 (1985);

S.B. Bumeliene, J. Pozhela, A.V. Tamasevicius: Phys. Status Solidi (b) 134, K71 (1986); J. Pozhela, Z.N. Tamaseviciene, A.V. Tamasevicius, J.K. Ulbikas, G.V. 'Bandurkina: Phys. Status Solidi (a) 110, 555 (1988)

2.25 P. Cvitanovic (ed.): Universality in Chaos (Adam Hilger, Bristol 1984) 2.26 O.E. Rossler: Phys. Lett. 71A, 155 (1979); Lect. App!. Math. 17, 141 (1979); Z. Naturforsch. 388,

788 (1983) 2.27 M. Duong-van (ed.): Proc. Int'! Conf. on the Physics of Chaos and Systems far from Equilib­

rium, Monterey, 1987 (North-Holland, Amsterdam 1987); special issue Nuc!. Phys. B (Proc. Supp!.) Vo!' 2 (1987)

2.28 A.R Bishop, G. Gruener, B. Niclaenko (eds.): Proc. Workshop on Spatio-Temporal Coherence and Chaos in Physical Systems, Los Alamos, 1986 (North-Holland, Amsterdam 1986); special issue Physica 23D (1986)

2.29 R.P. Huebener, K.M. Mayer, J. Parisi, J. Peinke, B. Rohricht: Nuc!. Phys. B (Proc. Supp!.) 2, 3 (1987); J. Peinke, J. Parisi, B. Rohricht, K.M. Mayer, U. Rau, RP. Huebener: Solid-State Electron. 31, 817 (1988)

2.30 K.M. Mayer, J. Parisi, J. Peinke, R.P. Huebener: Physica 32D, 306 (1988) 2.31 V.L. Bonch-Bruevich: Phys. Scr. T19, 491 (1987)

References 279

2.32 S.M. Sze: Physics of Semiconductor Devices (Wiley Eastern, New Delhi 1979) 2.33 K. Seeger: Semiconductor Physics, 5th edn. Springer Ser. Solid-State Sci., 'Vol. 40 (Springer,

Berlin, Heidelberg 1991) 2.34 R.1. Jones, P. Fisher: 1. Phys. Chem. Solids 26, 1125 (1965);

E.E. Haller, W.1. Hansen: Solid State Commun. 15,687 (1974); 1. S. Darken: J. Appl. Phys. 53, 3754 (1982)

2.35 RP. Huebener: In Advances in Electronics and Electron Physics, Vol. 70, ed. by P.W. Hawkes (Academic, New York 1988) p. 1

2.36 J. Peinke, J. Parisi, B. Rohricht, K.M. Mayer, U. Rau, W. ClauB, RP. Huebener, G. Jungwirt, W. Pretti: Appl. Phys. A 48, 155 (1989)

2.37 J. Parisi, U. Rau, 1. Peinke, K.M. Mayer: Z. Phys. B 72, 225 (1988); U. Rau, J. Parisi, K.M. Mayer, W. ClauB, J. Peinke, B. Rohricht, R P. Huebener: In Proc. 3rd Int'! Conf. on Shallow Impurities in Semiconductors, Linkoping, 1988, ed. by B. Monemar (Institute of Physics, Bristol 1989) p. 167

2.38 B. Rohricht, J. Parisi, J. Peinke, RP. Huebener: Z. Phys. B 66, 515 (1987); E. Scholl, J. Parisi, B. Rohricht, J. Peinke, R.P. Huebener: Phys. Lett. 119A, 419 (1987); E. Scholl, H. Naber, J. Parisi, B. Rohricht, J. Peinke, S. Uba: Z. Naturforsch. 44a, 1139 (1989)

2.39 W. Metzger, RP. Huebener, K.-P. Selig: Cryogenics 22, 387 (1982) 2.40 W. Monch: In Festkorperprobleme (Advances in Solid State Physics), Vol. 9, ed. by o. Madelung

(Vieweg, Braunschweig 1969) p. 172 2.41 H. Haken: Advanced Synergetics, Springer Ser. Syn., Vol. 20 (Springer, Berlin, Heidelberg 1983) 2.42 H. Haken: Information and Self-Organization, Springer Ser. Syn., Vol. 40 (Springer, Berlin,

Heidelberg 1988) 2.43 E. Scholl: Z. Phys. B 46, 23 (1982) 2.44 W. ClauB, J. Peinke, 1. Parisi, U. Rau, A. Kittel, RP. Huebener: Solid-State Electron. 32, 1197

(1989); W. ClauB, U. Rau, 1. Parisi, J. Peinke, Rp. Huebener, H. Leier, A. Forchel: J. Appl. Phys. 67, 2980 (1990)

2.45 J. Peinke, J. Parisi, A. Miihlbach, Rp. Huebener: Z. Naturforsch. 42a, 441 (1987) 2.46 K. Aoki, U. Rau, J. peinke, 1. Parisi, R.P. Huebener: J. Phys. Soc. Jpn. 59, 420 (1990);

U. Rau, K. Aoki, 1. Peinke, J. Parisi, W. ClauB, Rp. Huebener: Z. Phys. B 81, 53 (1990) 2.47 U. Rau, W. ClauB, A. Kittel, M. Lehr, M. Bayerbach, 1. Parisi, J. Peinke, Rp. Huebener: Phys.

Rev. B 43, 2255 (1991); A. Kittel, U. Rau, J. Peinke, W. ClauB, M. Bayerbach, 1. Parisi: Phys. Lett. 147A, 229 (1990)

2.48 D. Armbruster, G. Dangelmayr: Phys. Lett. 138A, 46 (1989) 2.49 E. Scholl: Physica 134B, 271 (1985); Phys. Rev. B34, 1395 (1986); 1. Phys. Chem. Solids 49,651

(1988); Phys. Scr. T29, 152 (1989); Solid-State Electron. 32, 1129 (1989) 2.50 J. Peinke, 1. Parisi, U. Rau, W. ClauB, M. Weise: Z. Naturforsch. 44a, 629 (1989) 2.51 B. Rohricht, 1. Parisi, J. Peinke, O.E. Rossler: Z. Phys. B 65, 259 (1986);

1. Parisi, J. Peinke, B. Rohricht, U. Rau, M. Klein, O.E. Rossler: Z. Naturforsch. 42a, 655 (1987); B. Rohricht, J. Parisi, J. Peinke, O.E. Rossler: Dynamics Stability Syst. 5, 99 (1990)

2.52 K.M. Mayer, R. Gross, 1. Parisi, J. Peinke, RP. Huebener: Solid State Commun. 63, 55 (1987); U. Rau, J. Peinke, 1. Parisi, RP. Huebener: Z. Phys. B 71, 305 (1988); U. Rau, K.M. Mayer, J. Parisi, 1. Peinke, W. ClauB, R.P. Huebener: Solid-State Electron. 32, 1365 (1989)

2.53 K.M. Mayer, R.P. Huebener, U. Rau: 1. Appl. Phys. 67, 1412 (1990)

Chapter 3

3.1 RH. Abraham, Ch.D .. Shaw: Dynamics, the Geometry of Behavior (Aerial, Santa Cruz 1983) 3.2 J. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of

Vector Fields, Appl. Math. Sci., Vol. 42 (Springer, Berlin, Heidelberg 1983)

280 References

3.3 H. Haken: Advanced Synergetics, Springer Ser. Syn., Vol. 20 (Springer, Berlin, Heidelberg 1983) 3.4 H.G. Schuster: Deterministic Chaos (Physik, Weinheim 1984) 3.5 P. Cvitanovic (ed.): Universality in Chaos (Adam Hilger, Bristol 1984) 3.6 B.-L. Hao (ed.): Chaos (World Scientific, Singapore 1984); Directions in Chaos, Vols. 1,2 (World

Scientific, Singapore 1987, 1988) 3.7 A.V. Holden (ed.): Chaos (Manchester University Press, Manchester 1986) 3.8 R.L. Devaney: An Introduction to Chaotic Dynamical Systems (Benjamin/Cummings, Menlo

Park, CA 1986) 3.9 J.M.T. Thompson, H.B. Stewart: Nonlinear Dynamics and Chaos (Wiley, Chichester, UK 1986) 3.10 P. Berge, Y. Pomeau, Ch. Vidal: Order within Chaos (Hermann, Paris 1986) 3.11 R.W. Leven, B.-P. Koch, B. Pompe: Chaos in dissipativen Systemen (Akademie, Berlin 1989) 3.12 E.N. Lorenz: J. Atmos. Sci. 20, 130 (1963) 3.13 J.-P. Eckmann: Rev. Mod. Phys. 53, 643 (1981) 3.14 J.D. Farmer, E. Ott, J.A. Yorke: Physica 7D, 153 (1983) 3.15 N.H. Packard, J.P. Crutchfield, J.D. Farmer, RS. Shaw: Phys. Rev. Lett. 45, 712 (1980);

F. Takens: In Dynamical Systems and Turbulence, Lect. Notes Math., Vol. 898, ed. by D.A. Rand, L.-S. Young (Springer, Berlin, Heidelberg 1981) p. 366

3.16 A.A. Andronov, L. Pontryagin: Dokl. Akad. Nauk. SSSR 14, 247 (1937) 3.17 C. Jacobi: Poggimd. Annal. 33, 229 (1834) 3.18 H. Poincare: Acta Math. 7, 259 (1885) 3.19 R. Thorn: Structural Stability and Morphogenesis (Benjamin, New York 1975) 3.20 J. Carr: Applications of Centre Manifold Theory, Appl. Math. Sci., Vol. 35 (Springer, Berlin,

Heidelberg 1981) 3.21 E.C. Zeeman: Catastrophe Theory (Addison-Wesley, Reading, MA 1977) 3.22 I. Stewart: Rep. Prog. Phys. 45, 185 (1982) 3.23 P.T. Saunders: Catastrophe Theory (Vieweg, Braunschweig 1986) 3.24 RP. Khosla, J.R Fischer, B.c. Burkey: Phys. Rev. B 7, 2551 (1973) 3.25 E. Scholl: Z. Phys. B 46, 23 (1982) 3.26 M. Lehr, R.P. Huebener, U. Rau, J. Parisi, W. ClauB, J. Peinke, B. Rohricht: Phys. Rev. B 42,

9019 (1990) 3.27 E. Hopf: Ber. Math.-Phys. Kgl. Sachs. Akad. Wiss. Leipzig 94, 1 (1942) 3.28 H.B. Stewart: Z. Naturforsch. 41a, 1412 (1986) 3.29 E.C. Zeeman: In Papers in Algebra, Analysis, and Statistics, ed. by R. Lidl (American Mathe-

matical Society, Providence, RI 1982) 3.30 J. Peinke, U. Rau, W. ClauB, R. Richter, J. Parisi: Europhys. Lett. 9, 743 (1989) 3.31 F.T. Arecchi, A. Lapucci, R. Meucci, J.A. Roversi, P.H. Coullet: Europhys. Lett. 6, 677 (1988) 3.32 M.M. Peixoto: Topology 1, 101 (1962) 3.33 P. Bak, T. Bohr, M.H. Jensen: In Directions in Chaos, Vol. 2, ed. by B.-L. Hao (World Scientific,

Singapore 1988) p. 16 3.34 M.H. Jensen, P. Bak, T. Bohr: Phys. Rev. A 30, 1960 (1984) 3.35 T. Bohr, P. Bak, M.H. Jensen: Phys. Rev. A 30, 1970 (1984) 3.36 K. Kaneko: Col/apse of Tori and Genesis of Chaos in Dissipative Systems (World Scientific,

Singapore 1986) 3.37 V.1. Arnol'd: Geometric Methods in the Theory of Ordinary Differential Equations, 2nd edn.,

Grundlehren math. Wissenschaften, Vol. 250 (Springer, Berlin, Heidelberg 1988) 3.38 H. Haucke, R Ecke: Physica 25D, 307 (1987);

M. Dubois: Nucl. Phys. B (Proc. Suppl.) 2, 339 (1987) 3.39 J. Parisi, J. Peinke, B. Rohricht, K.M. Mayer: Z. Naturforsch. 42a, 329 (1987);

J. Peinke, J. Parisi, B. Rohricht, B. Wessely, K.M. Mayer: Z. Naturforsch. 42a, 841 (1987) 3.40 U. Rau, J. Peinke, J. Parisi, RP. Huebener, E. Scholl: Phys. Lett. 124A, 335 (1987) 3.41 E.N. Lorenz: J. Atmos. Sci. 20, 130,448 (1963); Tellus 16, 1 (1964) 3.42 T.Y. Li, J.A. Yorke: Am. Math. Mon. 82, 985 (1975) 3.43 O.E. Rossler: Phys. Lett. 71A, 155 (1979); Lect. Appl. Math. 17, 141 (1979); Z. Naturforsch. 38a,

788 (1983)

3.44 O.E. Rossler: Phys. Lett. 57A, 397 (1976) 3.45 RS. Shaw: Z. Naturforsch. 36a, 80 (1981) 3.46 F. Hausdorff: Math. Ann. 79, 157 (1919) 3.47 MJ. Feigenbaum: J. Stat. Phys. 19, 25 (1978)

References 281

3.48 B.B. Mandelbrot: The Fractal Geometry of Nature (Freeman, San Francisco 1982) 3.49 E. Ott, E.D. Yorke, J.A. Yorke: Physica 16D, 62 (1985) 3.50 P. Grassberger, I. Procaccia: Physica 9D, 193 (1983) 3.51 A. Renyi: Probability Theory (North-Holland, Amsterdam 1970) 3.52 P. Grassberger, I. Procaccia: Physica 13D, 34 (1984) 3.53 P. Grassberger: Phys. Lett. 107A, 101 (1985) 3.54 R. Badii, A. Politi: J. Stat. Phys. 40, 725 (1985) 3.55 R. Stoop, J. Peinke, J. Parisi, B. Rohricht, R.P. Huebener: Physica 35D, 425 (1989) 3.56 G. Mayer-Kress (ed.): Dimensions and Entropies in Chaotic Systems, Springer Ser. Syn., Vol. 32

(Springer, Berlin, Heidelberg 1986) 3.57 J.-P. Eckmann, D. Ruelle: Rev. Mod. Phys. 57, 617 (1985) 3.58 T.e. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman: Phys. Rev. A33, 1141

(1986) 3.59 J.L. Kaplan, J.A. Yorke: In Functional Differential Equations and Approximation of Fixed

Points, Lect. Notes Math., Vol. 730, ed. by H.O. Peitgen, H.-e. Walther (Springer, Berlin, Heidelberg 1979) p. 204; P. Frederickson, J.L. Kaplan, E.D. Yorke. J.A. Yorke: J. Differ. Equ. 49,185 (1983)

3.60 P. Grassberger: In Chaos, ed. by A.V. Holden (Manchester University Press, Manchester 1986) p.291

3.61 K. Pawelzik, H.G. Schuster: Phys. Rev. A 35, 2207 (1987) 3.62 J.-P. Eckmann, I. Procaccia: Phys. Rev. A 34, 659 (1986) 3.63 M. Simo, S. Sato, Y. Sawada: Prog. Theor. Phys. 76, 945 (1986) 3.64 S. Grossmann, S. Thomae: Z. Naturforsch. 32a, 1353 (1977) 3.65 Y. Pomeau, P. Manneville: Commun. Math. Phys. 77, 189 (1980) 3.66 D. Ruelle, F. Takens: Commun. Math. Phys. 20, 167 (1971) 3.67 S. Newhouse, D. Ruelle, F. Takens: Commun. Math. Phys. 64, 35 (1978) 3.68 C. Grebogi, E. Ott, J.A. Yorke: Phys. Rev. Lett. 51, 339 (1983) 3.69 S.W. Teitsworth, RM. Westervelt, E.E. Haller: Phys. Rev. Lett. 51, 825 (1983) 3.70 J. Peinke, A. Miihlbach, RP. Huebener, J. Parisi: Phys. Lett. 108A, 407 (1985) 3.71 R ~ichter: Diploma Thesis, Tiibingen (1989) 3.72 J.Y. Huang, J.J. Kim: Phys. Rev. A 36, 1495 (1987) 3.73 J. Sacher, W. Elsasser, E.O. Gobel: Phys. Rev. Lett. 63, 2224 (1989) 3.74 M. Dubois, M.A. Rubio, P. Berge: Phys. Rev. Lett. 51, 1446 (1983) 3.75 G. Baier, K. Wegmann, J.L. Hudson: Phys. Lett. 141A, 340 (1989) 3.76 R. Richter, J. Peinke, W. ClauB, U. Rau, J. Parisi: Europhys. Lett. 14, 1 (1991) 3.77 J.E. Hirsch. B.A. Huberman, DJ. Scalapino: Phys. Rev. A 25, 519 (1982) 3.78 P. Manneville: J. de Phys. 41, 1235 (1980) 3.79 e. Grebogi, E. Ott, J.A. Yorke: Physica 7D, 181 (1983) 3.80 MJ. Feigenbaum, L.P. Kadanoff, SJ. Shenker: Physica 5D, 370 (1982) 3.81 SJ. Shenker: Physica 5D, 405 (1982) 3.82 A.P. Fein, M.S. Heutmaker, J.P. Gollub: Phys. Scr. T9. 79 (1985) 3.83 M.H. Jensen, L.P. Kadanoff, A. Libchaber, I. Procaccia, J. Stavans: Phys. Rev. Lett. 55, 2798

(1985) 3.84 G.A. Held, e. Jeffries: Phys. Rev. Lett. 56, 1183 (1986) 3.85 E.G. Gwinn, RM. Westervelt: Phys. Rev. Lett. 57, 1060 (1986); ibid. 59, 157,247 (1987) 3.86 Y. Kim: Phys. Rev. A 39, 4801 (1989) 3.87 J. Peinke, J. Parisi, R.P. Huebener, M. Duong-van, P. Keller: Europhys. Lett. 12, 13 (1990) 3.88 A.R. Bishop, G. Gruener, B. Nic\aenko (eds.): Proc. Workshop on Spatio-Temporal Coherence

and Chaos in Physical Systems, Los Alamos, 1986 (North-Holland, Amsterdam 1986); special issue Physica 23D (1986)

282 References

3.89 P. Keller, M. Duong-van: Nucl. Phys. B (Proc. Suppl.) 2, 603 (1987) 3.90 J.P. Crutchfield, K. Kaneko: In Directions in Chaos, Vol. 1, ed. by B.-L. Hao (World Scientific,

Singapore 1987) p. 271 3.91 K. Kaneko: Physica 34D, 1 (1989) 3.92 A. Brandl, W. Kroninger, W. Pretti, G. Obermair: Phys. Rev. Lett. 64, 212 (1990)

Chapter 4

4.1 P. Cvitanovic (ed.): Universality in Chaos (Adam Hilger, Bristol 1985); B.-L. Hao (ed.): Chaos (World Scientific, Singapore 1984)

4.2 B.B. Mandelbrot: The Fractal Geometry of Nature (Freeman, New York 1982) 4.3 J.-P. Eckmann, D. Ruelle: Rev. Mod. Phys. 57, 617 (1985);

for related topics, see [4.47-49] and O.E. Lanford: Statistical Mechanics, C.I.M.E. Lectures (Birkhiiuser, Boston 1976)

4.4 P. Boesiger, E. Brun, D. Meier: Phys. Rev. Lett. 38, 602 (1977); E. Brun, B. Derighetti, M. Ravani, G. Broggi, P,F. Meier, R. Stoop: Phys. Scr. T13, 119 (1986)

4.5 J. Peinke, A. Miihlbach, B. Rohricht, B. Wessely, 1. Mannhart, J. Parisi, R. P. Huebener: Physica 23D, 176 (1986); K.M. Mayer, J. Parisi,1. Peinke, R.P. Huebener: Physica 32D, 306 (1988)

4.6 C. Sparrow: The Lorenz Equations, Appl. Math. Sci., Vol. 41 (Springer, Berlin, Heidelberg 1982)

4.7 R.L. Devaney: An Introduction to Chaotic Dynamical Systems (Benjamin, Menlo Park, CA 1986)

4.8 M. Henon: Commun. Math. Phys. 50, 69 (1976) 4.9 P. Billingsley: Ergodic Theory and Information (Wiley, New York 1965);

V.I. Arnold, A. Avez: Ergodic Problems of Classical Mechanics (Benjamin, New York 1968); P. Walters: Ergodic Theory, Introductory Lectures, Lect. Notes Math., Vol. 458 (Springer, Berlin, Heidelberg 1975); M. Denker, C. Grillenberger, K. Sigmund: Ergodic Theory on Compact Spaces, Lect. Notes Math., Vol. 527 (Springer, Berlin, Heidelberg 1976); M. Reed, B. Simon: Functional Analysis (Academic, London 1972)

4.10 Z. Nitecki: Differentiable Dynamics (MIT Press, Cambridge, MA 1971) 4.11 J.D. Farmer, E. Ott, 1.A. Yorke: Physica 70,153 (1983) 4.12 A. Katok, J.-M. Strelcyn: Invariant Manifolds, Entropy and Billards; Smooth Maps with

Singularities, Lect. Notes Math., Vol. 1222 (Springer, Berlin, Heidelberg 1986) 4.13 T. Bohr, T. Tel: In Directions in Chaos, Vol. 2, ed. by B.-L. Hao (World Scientific, Singapore

1988) 4.14 S. Newhouse: Dynamical Systems, C.I.M.E. Lectures on Dynamical Systems (Birkhiiuser,

Boston 1980) 4.15 1. Guckenheimer, P. Holmes: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of

Vector Fields, Appl. Math. Sci., Vol. 42 (Springer, Berlin, Heidelberg 1986) 4.16 R. Lozi: J. de Phys. 39, 9 (1978) 4.17 H. Fujisaka: Prog. Theor. Phys. 70, 1264 (1983) 4.18 P. Grassberger, I. Procaccia: Physica 13D, 34 (1984) 4.19 H.E. Stanley: Introduction to Phase Transitions and Critical Phenomena, 2nd edn. (Oxford

University Press, New York 1987) 4.20 H.E. Stanley: In Statistical Mechanics and Field Theory, ed. by R.N. Sen, C. Wei! (Halsted,

New York 1972) 4.21 P. Collet, J.-P. Eckmann: Iterated Maps on the Interval as Dynamical Systems (Birkhiiuser,

Boston 1980)

References 283

4.22 M.J. Feigenbaum: J. Stat. Phys. 21, 669 (1979) 4.23 P. Grassberger: In Complex Systems, 12th Gwatt workshop, Internal Report (1988) 4.24 P. Cvitanovic, G. Gunaratne, l. Procaccia: Phys. Rev. A 38, 1503 (1988);

G. Gunaratne, M.H. Jensen, I. Procaccia: Nonlinearity 1, 157 (1988) 4.25 P. Grassberger, H. Kantz: Phys. Lett. 113A. 235 (1985) 4.26 A. Cohen, I. Procaccia: Phys. Rev. A 51, 1872 (1985) 4.27 M.J. Feigenbaum: Commun. Math. Phys. 77, 65 (1980) 4.28 A.B. Pippard: The Elements of Classical Thermodynamics (Cambridge University Press,

Cambridge 1957); D. Ruelle: Statistical Mechanics (Benjamin, Reading, MA 1969); A. Munster: Statistical Thermodynamics, Vol. 1 (Springer, Berlin, Heidelberg 1969)

4.29 T.e. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B. Shraiman: Phys. Rev. A 33,1141 (1986)

4.30 M. Kohmoto: Phys. Rev. A 37, 1345 (1988) 4.31 Y. Dono, Y. Takahashi: Prog. Theor. Phys. 63, 1804 (1980) 4.32 V.N. Shtern: Dokl. Akad. Nauk. SSSR 270, 582 (1983) 4.33 F. Hausdorff: Math. Ann. 79, 157 (1919) 4.34 H.G. Hentschel, 1 Procaccia: Physica 8D, 435 (1983) 4.35 L.P. Kadanoff, C. Tang: Proc. Natl. Acad. Sci. USA 81, 1276 (1984) 4.36 T. Yoshida, B. Chol So: Prog. Theor. Phys. 79, 1 (1988) 4.37 A. Renyi: Probability Theory (North-Holland, Amsterdam 1970) 4.38 P. Grassberger: Phys. Lett. 97A, 227 (1983) 4.39 P. Grassberger: Phys. Lett. 107A, 101 (1985) 4.40 R. Badii, A. Politi: Phys. Rev. Lett. 52, 1661 (1984) 4.41 G. Parisi: Appendix to "Fully developed turbulence and intermittency", by U. Frisch. In

Proc. Int'l School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, ed. by M. Ghil (North-Holland, Amsterdam 1984); U. Frisch: Phys. Scr. T9, 137 (1985)

4.42 M. Sano, S. Sato, Y. Sawada: Prog. Theor. Phys. 76, 945 (1986) 4.43 J.-P. Eckmann, I. Procaccia: Phys. Rev. A 34, 659 (1986) 4.44 R. Stoop, J. Peinke, J. Parisi, B. Rohricht, R.P. Huebener: Physica 35D, 425 (1989) 4.45 T. Horita, H. Hata, H. Mori, T. Morita, K. Tomita: Prog. Theor. Phys. 80, 923 (1988) 4.46 H.G. Schuster: Deterministic Chaos (Physik. Weinheim 1984) 4.47 Ya. G. Sinai: Russ. Math. Surv. 27, 21 (1972) 4.48 R. Bowen: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, Lect. Notes

Math., Vol. 470 (Springer, Berlin, Heidelberg 1975) 4.49 D. Ruelle: Thermodynamic Formolism. Encyclopedia of Mathematics and its Applications,

Vol. 5 (Addison-Wesley, Reading, MA 1978) 4.50 D. Katzen, I. Procaccia: Phys. Rev. Lett. 58, 1169 (1987) 4.51 M.J. Feigenbaum: J. Stat. Phys. 46, 919, 925 (1987) 4.52 M.H. Jensen, L.P. Kadanoff, I. Procaccia: Phys. Rev. A 36, 1409 (1987) 4.53 R.S. Ellis: Entropy, Large Deviations, and Statistical Mechanics, Grundlehren math.

Wissenschaften, Vol. 271 (Springer, Berlin, Heidelberg 1985) 4.54 P. Grassberger: In Proc. Conf. on Chaos in Astrophysics, Palm Coast, FL, 1984, ed. by

J. Perdang et aI. (Reid!, Dordrecht 1985); P. Grassberger: In Chaos, ed. by A.V. Holden (Manchester University Press, Manchester 1986)

4.55 R. Badii, A. Politi: Phys. Rev. A 35, 1288 (1987) 4.56 J.L. Kaplan, J.A. Yorke: In Functional Differential Equations and Approximation of Fixed

Points, Lect. Notes Math., Vol. 730, ed. by H.O. Peitgen, H.-C. Walther (Springer, Berlin, Heidelberg 1979) p. 204;

4.57 P. Fredrickson, J.L. Kaplan, E.D. Yorke, J.A. Yorke: J. Differ. Equ. 49, 185 (1983) 4.58 L.S. Young: J. Erg. Theor. Dyn. Syst. 2, 109 (1982)

284 References

4.59 H. Hata, T. Morita, K. Tomita, H. Mori: Prog. Theor. Phys. 78, 721 (1987) 4.60 R. Badii: Ph.D. Thesis, Zurich (1987) 4.61 P. Cvitanovic: In Proc. Workshop in Condensed Matter, Atomic and Molecular Physics,

Trieste, 1986, unpublished 4.62 T. Bohr, D. Rand: Physica 2SD, 387 (1987) 4.63 P. Grassberger: In Proc. Workshop on Dynamics of Fractals and Hierarchies of Critical

Exponents, Orsay, 1986, unpublished 4.64 M. Duong-van: Private communication (1988) 4.65 H. Hata, T. Horita, H. Mori, T. Morita, K. Tomita: Prog. Theor. Phys. SO, 809 (1988) 4.66 T. Horita, H. Hata, H. Mori, T. Morita, S. Kuroki, H. Okamoto: Prog. Theor. Phys. SO, 793

(1988) 4.67 D. Auerbach, P. Cvitanovic, J.-P. Eckmann, G. Gunaratne, I. Procaccia: Phys. Rev. Lett. 58,

2387 (1987) 4.68 P. Grassberger: Internal Report, University of Wuppertal (1988) 4.69 P. Szepfalusy, T. Tel, A. Csordas, Z. Kovacs: Phys. Rev. A 36, 3525 (1987) 4.70 H. Whitney: Ann. Math. 37, 645 (1936) 4.71 F. Takens: In Dynamical Systems and Turbulence, ed. by D.A. Rand, L.-S. Young, Lect. Notes

Math., Vol. 89~ (Springer, Berlin, Heidelberg 1981) p. 366 4.72 R. Mane: In Dynamical Systems and Turbulence, ed. by D.A. Rand, L.-S. Young. Lect. Notes

Math., Vol. 898 (Springer, Berlin, Heidelberg 1981) p. 230 4.73 J. Dieudonne: Treatise on Analysis, Vol. 3 (Academic, New York 1972);

S. Sternberg: Lectures on Differential Geometry (Prentice Hall, Englewood Cliffs, NJ 1964) 4.74 A.M. Fraser, R.L. Swinney: Phys. Rev. A 33, 1134 (1986) 4.75 A.M. Fraser: Ph.D. Thesis, Austin (1988) 4.76 R. Stoop, P.F. Meier: Nucl. Phys. B (Proc. Suppl.) 2, 582 (1987) 4.77 R. Stoop, P.F. Meier: J. Opt. Soc. Am. B 5, 1037 (1988) 4.78 V.I. Oseledec: Moscow Math. Soc. 19, 197 (1968) 4.79 G. Benettin, L. Galgani, J.M. Strelcyn: Phys. Rev. A 14, 2338 (1976) 4.80 J. Froyland, K.H. Alfsen: Internal Report, University of Oslo (1984);

I.M. Greene, 1.-S. Kim: Physica 24D, 213 (1987) 4.81 A. Wolf, J.A. Vastano: In Dimensions and Entropies in Chaotic Systems, ed. by G. Mayer-Kress,

Springer Ser. Syn., Vol. 32 (Springer, Berlin, Heidelberg 1986) 4.82 M. Sano, Y. Sawada: Phys. Rev. Lett. 55, 1082 (1985) 4.83 J.-P. Eckmann, S. Oliffson Kamphorst, D. Ruelle, S. Ciliberto: Phys. Rev. A 34, 4971 (1986) 4.84 T.M. Hegland: Private communication (1988) 4.85 G. Broggi, P.F. Meier, R. Stoop, R. Badii: Phys. Rev. A 35, 365 (1987) 4.86 H. Atmanspacher, H. Scheingraber: Phys. Rev. A 34, 253 (1985) 4.87 J.-P. Eckmann, D. Ruelle: Internal Report, I.R.E.S Bures-sur-Yvette (1989) 4.88 E.J. Kostelich, H.L. Swinney: In Chaos and Related Nonlinear Phenomena, ed. by I. Procaccia,

M. Shapiro (Plenum, New York 1987) 4.89 S. Sato, M. Sano, Y. Sawada: Prog. Theor. Phys. 77, 1 (1987) 4.90 R. Badii, G. Broggi, B. Derighetti, M. Ravani, S. Ciliberto, A. Politi, M.A. Rubio: Phys. Rev.

Lett. 60, 979 (1988) 4.91 R. Stoop, J. Parisi: Physica 500, 89 (1991) 4.92 R. Stoop, J. Parisi, J. Peinke: In A Chaotic Hierarchy, ed. by G. Baier, M. Klein (World

Scientific, Singapore 1991) p. 341 4.93 J. Stoer, R. Bulirsch: Introduction to Numerical Analysis (Springer, Berlin, Heidelberg 1980) 4.94 W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling: Numerical Recipes (Cambridge

University Press, Cambridge 1986) 4.95 J.M. Greene, J.-S. Kim: Physica 240, 213 (1987) 4.96 D.S. Broomhead, G.P. King: In Nonlinear Phenomena and Chaos, ed. by S. Sarkar (Adam

Hilger, Bristol 1986) 4.97 O.E. Rossler: Phys. Lett. 71A, 155,(1979)

References 285

4.98 E. Hopf: Topologie (Springer, Berlin, Heidelberg 1935) 4.99 P. Alexandroff: Combinatorial Topology, Vol. 3 (Graylock, Rochester 196(,)) 4.1(')(') H. Amann: Gewohnliche Differentialgleichungen (de Gruyter, Berlin 1983) 4.101 K. Deimling: Nichtlineare Gleichungen und Abbildungsgrade (Springer, Berlin, Heidelberg

1976) 4.102 H.G. Solari, R. Gilmore: Private communication (1988) 4.1(')3 V.I. Arnol'd: Geometrical Methods in the Theory of Ordinary Differential Equations, 2nd edn.,

Grundlehren math. Wissenschaften, Vol. 25(') (Springer, Berlin, Heidelberg 1988) 4.1(')4 H. Brauchli, H. Weber, R. Stoop: Unpublished 4.1(')5 D.V. Anasov: Tr. Steklov 90, 1 (1967) 4.106 J. Veerman: Physica A 134, 543 (1986)

Subject Index

Anosov flow 273 Arnold tongue 98,99, 106, 107 attraetor 47, 176 -, axiom A 179 - basin 47 -, fractal 126 -, strange 111, 126, 183

baker map 204-207 bifurcation 49-57 -, generalized Hopf 68 -, Hopf 50,52,66-72 -, Neimark 90 -, pitchfork 53-59,67, 135 - point 49, 135 -, saddle node 52-56,60,136-138 -, saddle node on a limit cycle 66-80, 92, 102,

136-138,147 -, saddle node on a torus 90, 136-138 -, secondary Hopf 90, 92 -, subcritical Hopf 68, 69 -, subcritical pitchfork 53-56, 67, 68 -, transcritical 53-56, 59, 60 blue sky catastrophe 66-73, 80, 81, 90, 147 Boltzmann equation 32 breakdown -, avalanche 11, 14, 16,25 - electric field 24-27 -, injection 14 - voltage 24-27

Cantor set 176, 177, 196-199,203 catastrophe theory 50, 56-60 center 44, 45 -, organizing 57 chaos 17,109-158,184,185 -, introduction to 1-8 -, routes to 17, 134-154 circle map 17,94-108, 134, 147LJ54 codimension 50, 57 complexity 201 conductance

-, negative differential (NDC) 12,13,25-27,32, 60-62

-, positive differential (PDC) 12, 13 conductivity -, negative differential (ndc) 11-13, 32 -, positive differential (pdc) 12, 13 conjugacy map 227, 228 control parameter 10,21-28,43,44,60-63 cooling effect 28 correlation function 149-154 crisis 147,234 -, boundary 147 -, heteroclinic 229 -, inner 147 crowding index 187 current-voltage characteristic 23-28, 30, 33,

60-63 cusp catastrophe 29, 58-63

degree of mapping 271-273 dimension 111,117-134 -, capacity 119 -, correlation 119, 120,215, 216 -, embedding 117-134,212,238 -,fractal 117-134 -, generalized 120-134,152-154,210-238 -, Hausdorff 111,114,119,197 -, information 120, 121, 129,215,216 -, local pointwise 187,201 -, Lyapunov 129,224,225,233 -, Renyi 120, 200, 210-238 -, topological 117-134 dissipation 42-44, Ill, 175 domain 12

embedding - space 117-134,212,240,265,266 - theorem 237, 238 enslaving principle 52, 155 entropy 120-134 -, generalized 129-134, 194,210-236,238 -, information-theoretical 190, 201, 207, 208,

222, 238

288 Subject Index

entropy, Kolmogorov-Sinai 130, 131, 189, 190, 202, 217

-, topological 130, 131, 189,216 escape rate 180, 198, 201, 217, 218

Farey tree 99, 100, 148 Fibonacci number 99, 100 filament 12, 35-38 -, breathing 32,34,154-156 filter technique 261 filtering exponent 194 fixed-mass method 212, 215, 219, 220 fixed point 44,45,53-63, 156, 157, 179, 180 fixed-size method 211 flow 4-8,44 focus 44,45 fractal 99, 117 -, uniform 197 free energy -, generalized 194 -, Gibbs 191 frequency-locking 82-108,134, 147-154,234 Frobenius-Perron equation 179,201 -, eigenfunction of 180, 233

generation-recombination process 32 golden mean 100,148-154

Han effect 25, 26 Henon map 7, 177,212,229, 244-251, 260, 261,

267 heteroc1inic intersection 182 homoclinic - intersection 182 - tangency point 182, 183, 229, 234, 243, 256 horseshoe map 183 hot carriers 14, 25 hyperbolicity 180, 204, 233 hyperchaos 17,109-158,252,256,269 hysteresis 25, 58, 59

impurity - impact ionization 25 - level 15, 19,20, 32 information 120-134 -, generalized 120-134 -, Renyi 120--134 -, Shannon 120, 190 instability 9-11 -, Alfven 11 -, domain 16 -, Gunn 14 -, helicon 11, 16 -, plasma 10,11,16

-, spatial 17,35-38 -, spatio-temporal 17,38-40,154-168 -, temporal 17,28-35 -, two-stream 11 intermittency 17,136-147,234 -, type I 136-139 -, type II 139, 140 -, type III 140-146 Ising model 219,227

Kaplan-Yorke conjecture 129,224,225,261

laminar - length 138-146 - phase 136-146 Landau-Hopf model 115, 122 laser - experiment 236,251-255,262,263 - model 245-251 limit cycle 64, 154-163 load resistor 10, 62, 63 Lobachevski plane 273 logistic map 114, 134-139, 147, 186, 187,226,

227 Lorenz system 175,231,244-251,260-262,268,

269 Lozi map 183, 184 Lyapunovexponent 113, 114, 128-134, 185,

187, 198,201,214-217,224,238-271 -, generalized 214,215

magnetoresistive effect 28 manifold -, center 51,52, 128 -, stable 51,52,128, 180-183,248 -, unstable 51,52,128,177,180-184,248 Markov - Kakutani theorem 179 measure -, ergodic 179 -, natural 119-134, 179 -, probability 177, 178 -, SRB 179,225 measuring configuration 21-23, 86-89, 155,

156, 159-161 mixing component 92,93,104-107,153, 166,

167

node 44,45 nonhyperbolicity 180

observable 43, 178 ohmic contact 19, 20 omega explosion 69 ordinary differential equation 42-44

oscillation - center 38-40,154-168 -, chaotic 17, 109-158 -, hyperchaotic 17, 109-158,252,256,269 -, periodic 63-82 -, quasiperiodic 17,82-108,134,147-168 -, relaxation 29, 30 -, spontaneous 30-35 -, switching 29,63

partition function 125, 191, 194,206,218,231 Pesin's formula 208, 222 phase - diagram 73,80,91,98, 107 - portrait 44,64,84-89,118,119,127,156,157 - space 44 - transition 126,132-134,191,192,219,

226-236 plasma 10, 11 - instability 10, 11 Poincare - cross section 85-90, 94, 112-115, 175 - map 85 power spectrum 64-66,115,116, 149-152 principal tangency point 190

Rashevsky-Turing theory 35 recurrence 5-8, 47, 85 relaxation time 33 repeller 44, 45, 201, 227 reproducibility 23 resonance imaging 39, 40 return map 85-90,96, 113-115, 134-139 Rossler system 5-8, 11 0-114

saddle 44,45, 181,219, 229 saddle point approach 194, 195,212,219 sample - geometry 20,21 - material 19 scale invariance 186 scaling - exponent 17, 123-134, 152-154, 186,222

Subject Index 289

- function 17,123-134,152-154,190, 210-236, 246-251, 258, 259'

- index 17, 123-134, 152-154, 186,222 scanning electron microscopy 22, 23, 35-40 scenario 17, 134-154 -, Feigenbaum-Grossmann 17, 134-136 -, frequency-locking 134,147-154 -, Pomeau-Manneville 17,134,136-147 -, Rossler 17 -, Ruelle-Takens-Newhouse 17, 134 self-affinity 196 self-organization 3, 159, 168 self-similarity 185, 186, 195 shift map 189 singular-value decomposition 263,,264 sink 44,45 slowing down 34, 35, 73, 136, 137 source 44, 45 stability -, linear analysis of 51 -, Lyapunov 44,45 -, orbit 46 -, structural 48,49, 183 stroboscopic plot 86-90, 118, 119 support 178 symbolic dynamics 188, 200 synergetics 35, 155, 159, 168

taffy puller 4-8 Takens-Crutchfield construction 48, 85-90,

121, 131, 237, 238 tent map 188, 189, 202, 216, 248 thermodynamical - analogy 190-193, 196,218-221,226 - formalism 125-134,171-236 - limit 193 torus 83, 84 trajectory 44 transient 47 transport mechanism 13-15

van der Waals gas 59, 191, 192

winding number 98, 106, 107