On the basin problem for Hénon-like attractors

Research output: Contribution to journalArticle

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Abstract

The basin problem for a strange attractor asks the asymptotic distribution of Lebesgue almost every initial point in the basin of attraction. A solution to this problem for Hénon-like attractors was initially given by Benedicks-Viana, and later by Wang-Young, under certain assumptions on the Jacobian of the map, which are used in a crucial way to control the growth of volumes under iteration. The purpose of this paper is to remove the assumption on the Jacobian in their solutions, in a hope that the argument can be extended to a broader class of Hénon-like maps which are not necessarily invertible and possess singularities.

Original languageEnglish
Pages (from-to)303-348
Number of pages46
JournalJournal of Mathematics of Kyoto University
Volume46
Issue number2
Publication statusPublished - 2006
Externally publishedYes

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Attractor
Strange attractor
Basin of Attraction
Henri Léon Lebésgue
Invertible
Asymptotic distribution
Singularity
Iteration
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the basin problem for Hénon-like attractors. / Takahasi, Hiroki.

In: Journal of Mathematics of Kyoto University, Vol. 46, No. 2, 2006, p. 303-348.

Research output: Contribution to journalArticle

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