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Basin problem for Hénon-like attractors in arbitrary dimensions

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  • We prove that Hénon-like strange attractors of diffeomorphisms in any dimensions, such as considered in [2], [7], and [9] support a unique Sinai-Ruelle-Bowen (SRB) measure and have the no-hole property: Lebesgue almost every point in the basin of attraction is generic for the SRB measure. This extends two-dimensional results of Benedicks-Young [4] and Benedicks-Viana [3], respectively.
    Mathematics Subject Classification: Primary: 37D45; Secondary: 37C40, 37D25, 37E99.


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