On the basin problem for Hénon-like attractors

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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
JournalKyoto Journal of Mathematics
Volume46
Issue number2
DOIs
Publication statusPublished - 2006 Jan 1

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ASJC Scopus subject areas

  • Mathematics(all)

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