Korteweg-de Vries Institute for Mathematics

General Mathematics Colloquium

11Mar2015 11:15 - 12:15

Event

Speaker: Han Peters (KdVI)

Title: A polynomial map with wandering Fatou components.

Abstract

In 1982 Dennis Sullivan proved his famous non-wandering domains theorem, stating that for a rational function every Fatou component is either periodic or pre-periodic. His result completed the classification of Fatou components, and brought new tools to complex dynamical systems that have had an enormous impact on the field.

Sullivan's theorem has been generalized to real polynomials by Martens, de Melo and van Strien, and to classes of entire maps by Lyubich and Eremenko and by Goldberg and Keen. In higher dimensions the questions remained open.

In joint work with Matthieu Astorg, Xavier Buff, Romain Dujardin and Jasmin Raissy, based on an idea of Misha Lyubich, we prove the existence of polynomial maps with wandering Fatou components. Our maps are polynomial skew products in two complex variables, and the main tool in the proof is the theory of parabolic implosion. This talk is not meant for experts in complex analysis or dynamical systems.

 

Location: KdVI Meeting Room (Science Park 105-107,  F3.20)

 

Published by  Korteweg de Vries Institute