Journal of Mathematics of Kyoto University

On the basin problem for Hénon-like attractors

Hiroki Takahasi

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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.

Article information

J. Math. Kyoto Univ., Volume 46, Number 2 (2006), 303-348.

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37D45: Strange attractors, chaotic dynamics
Secondary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces


Takahasi, Hiroki. On the basin problem for Hénon-like attractors. J. Math. Kyoto Univ. 46 (2006), no. 2, 303--348. doi:10.1215/kjm/1250281779.

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