Resurgence of Receding Limbs

Resurgence of Receding Limbs

Ergodic Methods in DynamicsBedlewo April 24. 2012

Carsten Lunde PetersenNSM RUC

• Joint work Adam Epstein, Warwick University

0

1/4

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1/3 Limb1/7

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Zoom on 1/3 Limb and wake

1/2

3/4 1/4

1/3 wake and Limb with dyadic

sub-wakes

M1/3 in purple

Sub wakes of 1/3 Limb

3/41/4

1/2

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•This explains the notion of Limbs in the Mandelbrot set and its dyadic decorations.

•Now we come to the Main topic Quadratic rational maps.

M0,5, σ2-plane

M0 M0.8

M0.9 M1

(-75+33i::5-27i)

(245+108.75i::5-78.75i)

(-7000+3000i::1000-3000i)

M1

The End