BRANNER-HUBBARD Motion without Dynamics

Congress in the Memory of

Adrien Douady,

Paris,

May 2008.

Michel Zinsmeister, MAPMO, UMR 6628,Orléans, France

Adrien Douady’s last work:

Branner-Hubbard Motion without Dynamics.

2) Branner Hubbard Motion.

3) Conjectures, perspectives and some results

1) The harmonic Atlas

4) Link with multifractality

1) The harmonic Atlas

and =0 on K

The historical example: Quadratic polynomials.

2) The Branner-Hubbard Motion

BRANNER-HUBBARD Motion:

3) Conjectures and some results.

homeomorphic to a planar full compact set with empty interior.

c1 c2 c3

G(c1)

G(c2)

G(c3)

4) Connection with multifractality

b

a

Thanks to Arnaud Chéritat for the computer pictures.