Coexistence of invariant sets with and without SRB measures in Hénon family

Shin Kiriki*, Ming-Chia Li, Teruhiko Soma

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Let {fa,b} be the (original) Hénon family. In this paper, we show that, for any b near 0, there exists a closed interval Jb which contains a dense subset J' such that, for any a ∈ J' , f a,b has a quadratic homoclinic tangency associated with a saddle fixed point of fa,b which unfolds generically with respect to the oneparameter family {fa,b}a∈Jb . By applying this result, we prove that Jb contains a residual subset A(2) b such that, for any a ∈ A(2) b , f a,b admits the Newhouse phenomenon. Moreover, the interval J b contains a dense subset Ãb such that, for any a ∈ Ãb, fa,b has a large homoclinic set without SRB measure and a small strange attractor with SRB measure simultaneously.

Original languageEnglish
Pages (from-to)2253-2269
Number of pages17
JournalNonlinearity
Volume23
Issue number9
DOIs
StatePublished - 1 Sep 2010

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