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Absolutely continuous invariant measures for multidimensional expanding maps

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Abstract

We investigate the existence and statistical properties of absolutely continuous invariant measures for multidimensional expanding maps with singularities. The key point is the establishment of a spectral gap in the spectrum of the transfer operator. Our assumptions appear quite naturally for maps with singularities. We allow maps that are discontinuous on some extremely wild sets, the shape of the discontinuities being completely ignored with our approach.

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  1. Benoît Saussol

    Present address: Department de Matemática, Instituto Superior Técnico, Avenida Rovisco Pais, 1049-001, Lisboa, Portugal

Authors and Affiliations

  1. Centre de Physique Théorique, Unité Propre de Recherche 7061, CNRS Luminy, Case 907, F-13288, Marseille-Cedex 9, France

    Benoît Saussol

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  1. Benoît Saussol
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Saussol, B. Absolutely continuous invariant measures for multidimensional expanding maps. Isr. J. Math. 116, 223–248 (2000). https://doi.org/10.1007/BF02773219

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  • DOI: https://doi.org/10.1007/BF02773219

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