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Solution of the basin problem for Hénon-like attractors

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Inventiones mathematicae Aims and scope

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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Authors and Affiliations

  1. KTH, Department of Mathematics, 100 44 Stockholm, Sweden (e-mail: michaelb@math.kth.se), , , , , , SE

    Michael Benedicks

  2. IMPA, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro RJ, Brasil (e-mail: viana@impa.br), , , , , , BR

    Marcelo Viana

Authors
  1. Michael Benedicks
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  2. Marcelo Viana
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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

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