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Expansive homeomorphisms of surfaces

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Abstract

Letf be an expansive homeomorphism of a compact oriented surfaceM. We show thatS 2 does not support such anf, and thatf is conjugate to an Anosov diffeomorphism ifM=T 2, and to a pseudo-Anosov map ifM has genus ≥2. These results are consequences of our description of local stable (unstable) sets: everyx∈M has a local stable (unstable) set that consists of the union ofr arcs that meet only atx. For eachx∈M r=2, except for a finite number of points, wherer≥3.

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Authors and Affiliations

  1. Instituto de Matemática y Estadística Prof. Ing. Rafael Laguardia, Montevideo, Uruguay

    Jorge Lewowicz

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  1. Jorge Lewowicz
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Lewowicz, J. Expansive homeomorphisms of surfaces. Bol. Soc. Bras. Mat 20, 113–133 (1989). https://doi.org/10.1007/BF02585472

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  • DOI: https://doi.org/10.1007/BF02585472

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