Abundance of non-uniform hyperbolicity in bifurcations of surface endomorphisms

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Abstract

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.

Original languageEnglish
Pages (from-to)53-113
Number of pages61
JournalTokyo Journal of Mathematics
Volume34
Issue number1
DOIs
Publication statusPublished - 2011 Jan 1
Externally publishedYes

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ASJC Scopus subject areas

  • Mathematics(all)

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