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Nonexistence of Wandering Domains for Infinitely Renormalizable Hénon Maps
Başlık:
Nonexistence of Wandering Domains for Infinitely Renormalizable Hénon Maps
Yazar:
Ou, Dyi-Shing, author.
ISBN:
9780438148406
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (235 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-11(E), Section: B.
Advisors: Marco Martens Committee members: Eric Bedford; Michael Benedicks; Mikhail Lyubich.
Özet:
In the thesis, I proved the absence of wandering domains for strongly dissipative infinitely renormalizable Henon-like maps with arbitrary stationary combinatorics. The theorem solves an open problem proposed by van Strien (2010) and Lyubich and Martens (2011) and opens a direction of studying the existence of wandering domains in higher-dimensional systems. Unimodal maps are a reduced version of Henon-like maps in one-dimension and unimodal maps do not have wandering intervals. However, the classical proofs for unimodal maps break down in the Henon setting. To resolve this issue, two higher-dimensional techniques, "the area argument" and "the good region and the bad region", are introduced in the thesis to prove the theorem.
The proof is split into two cases. The first case covers infinitely period-doubling renormalizable Henon-like maps. The second case covers infinitely renormalizable Henon-like maps with stationary combinatorics other than period-doubling. The difference between the proofs of the two cases comes from the way of how we measure the expansion of a set when it is iterated under a Henon-like map. The prior case relies on the Euclidean metric, and the later case relies on the hyperbolic metric. The two cases are disjoint, and together solve the problem for all stationary combinatorics.
As an application, the theorem enriches our understanding about the topological structure of the heteroclinic web: the union of the stable manifolds forms a dense set in the domain.
Notlar:
School code: 0771
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
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XX(693810.1) | 693810-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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