|主講者:||Professor Dyi-Shing Ou (Polish Academy of Sciences)|
|講題:||Nonexistence of Wandering Domains for Infinitely Renormalizable Henon Maps|
|時間:||2020-01-03 (Fri.) 16:00 - 17:00|
|地點:||數學所 722 研討室 (台大院區)|
|Abstract:||Henon-like maps are generalizations of unimodal maps from one to two dimensions. It is known that unimodal maps do not have a wandering domain.
The main difficulty of generalizing the theorem to Henon-like maps comes from
nonhyperbolicity . In this talk, we consider a type of Henon-like maps, called
infinitely renormalizable maps with stationary combinatorics [3, 4]. I will explain how to resolve the problem that comes from nonhyperbolicity and prove
the theorem: an infinitely renormalizable Henon-like map with stationary combinatorics do not have a wandering domain [1, 2]. This solves an open problem
proposed by van Strien (2010)  and Lyubich and Martens (2011) . As an
application, the theorem enriches our understanding of the topological structure of the heteroclinic web: the union of the stable manifolds of periodic orbits
forms a dense set in the domain.
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