主講者:  Professor DyiShing Ou (Polish Academy of Sciences) 
講題:  Nonexistence of Wandering Domains for Infinitely Renormalizable Henon Maps 
時間:  20200103 (Fri.) 16:00  17:00 
地點:  數學所 722 研討室 (台大院區) 
Abstract:  Henonlike 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 Henonlike maps comes from
nonhyperbolicity [6]. In this talk, we consider a type of Henonlike 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 Henonlike map with stationary combinatorics do not have a wandering domain [1, 2]. This solves an open problem
proposed by van Strien (2010) [5] and Lyubich and Martens (2011) [6]. 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.
References

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