Abundance of non-uniform hyperbolicity in bifurcations of surface endomorphisms

研究成果: Article査読

10 被引用数 (Scopus)

抄録

We study an interplay between homoclinic behavior and singularities in surface endomorphisms. We show that appropriate rescalings near homoclinic orbits intersecting fold singularities yield families of noninvertible Hénon-like maps. Then we construct positive measure sets of parameters corresponding to maps which exhibit nonuniformly hyperbolic behavior. This implies an extension of the celebrated theorem of Benedicks and Carleson, and that of Mora and Viana to surface endomorphisms.

本文言語English
ページ(範囲)53-113
ページ数61
ジャーナルTokyo Journal of Mathematics
34
1
DOI
出版ステータスPublished - 2011
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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