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.
Citation
Hiroki Takahasi. "On the basin problem for Hénon-like attractors." J. Math. Kyoto Univ. 46 (2) 303 - 348, 2006. https://doi.org/10.1215/kjm/1250281779
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