Abstract.
For a large class of non-uniformly hyperbolic attractors of dissipative diffeomorphisms, we prove that there are no “holes” in the basin of attraction: stable manifolds of points in the attractor fill-in a full Lebesgue measure subset. Then, Lebesgue almost every point in the basin is generic for the SRB (Sinai-Ruelle-Bowen) measure of the attractor. This solves a problem posed by Sinai and by Ruelle, for this class of systems.
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Oblatum 30-IX-1999 & 8-VI-2000¶Published online: 18 September 2000
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Benedicks, M., Viana, M. Solution of the basin problem for Hénon-like attractors. Invent. math. 143, 375–434 (2001). https://doi.org/10.1007/s002220000109
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DOI: https://doi.org/10.1007/s002220000109