dinamicna analizaˇ€¦ · • dinamika – stabilnost ciklov 8 – eksponenti ljapunova 13 –...
TRANSCRIPT
![Page 1: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/1.jpg)
Marko Znidaric
DINAMICNA ANALIZA
Zapiski predavanj
Univerza v Ljubljani
Fakultete za Matematiko in Fiziko
Oddelek za Fiziko
2010
![Page 2: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/2.jpg)
Dinamicna analiza, dodiplomski studij, 2009/2010
Kazalo
• Uvod 3
Opozorilo: Uvodni del je kratek. Za prvih nekaj poglavij, do naslednjega
v teh zapiskih, ki opisejo in definirajo preproste dinamicne sisteme, stro-
boskopske preslikave, Poincarejeve secne ploskve, itd., glej npr. skripto
”Dinamicna Analiza: Uvod v teorijo deterministicnega kaosa” Tomaza
Prosena!
• Globalna struktura – geometrija
– Cantorjeve mnozice 5
• Dinamika
– Stabilnost ciklov 8
– Eksponenti Ljapunova 13
– Statisticne lastnosti 18
– Entropija 27
– Markovski procesi 34
– Simbolicna dinamika 39
• 1D preslikave 44
• Hamiltonski sistemi
– Splosne lastnosti 50
– Integrabilnost 55
– Hamilton-Jacobijev formalizem 57
– Biljardi 60
– Prehod od integrabilnosti do kaosa 65
– Homoklinske tocke 74
• Vecdelcni sistemi 76
![Page 3: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/3.jpg)
![Page 4: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/4.jpg)
![Page 5: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/5.jpg)
![Page 6: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/6.jpg)
![Page 7: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/7.jpg)
![Page 8: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/8.jpg)
![Page 9: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/9.jpg)
![Page 10: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/10.jpg)
![Page 11: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/11.jpg)
![Page 12: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/12.jpg)
![Page 13: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/13.jpg)
![Page 14: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/14.jpg)
![Page 15: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/15.jpg)
![Page 16: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/16.jpg)
![Page 17: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/17.jpg)
![Page 18: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/18.jpg)
![Page 19: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/19.jpg)
![Page 20: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/20.jpg)
![Page 21: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/21.jpg)
![Page 22: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/22.jpg)
![Page 23: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/23.jpg)
![Page 24: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/24.jpg)
![Page 25: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/25.jpg)
![Page 26: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/26.jpg)
![Page 27: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/27.jpg)
![Page 28: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/28.jpg)
![Page 29: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/29.jpg)
![Page 30: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/30.jpg)
![Page 31: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/31.jpg)
![Page 32: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/32.jpg)
![Page 33: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/33.jpg)
![Page 34: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/34.jpg)
![Page 35: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/35.jpg)
![Page 36: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/36.jpg)
![Page 37: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/37.jpg)
![Page 38: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/38.jpg)
![Page 39: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/39.jpg)
![Page 40: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/40.jpg)
![Page 41: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/41.jpg)
![Page 42: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/42.jpg)
![Page 43: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/43.jpg)
![Page 44: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/44.jpg)
![Page 45: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/45.jpg)
![Page 46: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/46.jpg)
![Page 47: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/47.jpg)
![Page 48: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/48.jpg)
![Page 49: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/49.jpg)
![Page 50: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/50.jpg)
![Page 51: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/51.jpg)
![Page 52: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/52.jpg)
![Page 53: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/53.jpg)
![Page 54: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/54.jpg)
![Page 55: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/55.jpg)
![Page 56: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/56.jpg)
![Page 57: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/57.jpg)
![Page 58: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/58.jpg)
![Page 59: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/59.jpg)
![Page 60: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/60.jpg)
![Page 61: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/61.jpg)
![Page 62: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/62.jpg)
![Page 63: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/63.jpg)
![Page 64: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/64.jpg)
![Page 65: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/65.jpg)
![Page 66: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/66.jpg)
![Page 67: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/67.jpg)
![Page 68: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/68.jpg)
![Page 69: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/69.jpg)
![Page 70: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/70.jpg)
![Page 71: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/71.jpg)
![Page 72: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/72.jpg)
![Page 73: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/73.jpg)
![Page 74: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/74.jpg)
![Page 75: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/75.jpg)
![Page 76: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/76.jpg)
![Page 77: DINAMICNA ANALIZAˇ€¦ · • Dinamika – Stabilnost ciklov 8 – Eksponenti Ljapunova 13 – Statistiˇcne lastnosti 18 – Entropija 27 – Markovski procesi 34 – Simboliˇcna](https://reader033.vdocuments.site/reader033/viewer/2022060607/605dfd296110ab454f477625/html5/thumbnails/77.jpg)