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A classification of minimal sets for surface homeomorphisms

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Abstract

We classify minimal sets of (closed and oriented) hyperbolic surface homeomorphisms by studying the connected components of their complement. This extends the classification given by Jäger et al. (Mat Z 274(1–2):405–426, 2013) in the torus. The classification being sensitive to global topology, striking differences with the toral case arise. We also show that the given classification can be strengthened when considered for non-wandering (conservative) systems, and in the homotopy class of pseudo-Anosov maps.

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Notes

  1. Here a usual abuse of notation is done in order to get the sets defined.

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Acknowledgments

We would like to thank the referee for numerous suggestions, which helped to clarify several proofs throughout this article.

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  1. UdelaR, Montevideo, Uruguay

    Alejandro Passeggi & Juliana Xavier

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  1. Alejandro Passeggi
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  2. Juliana Xavier
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Correspondence to Alejandro Passeggi.

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Passeggi, A., Xavier, J. A classification of minimal sets for surface homeomorphisms. Math. Z. 278, 1153–1177 (2014). https://doi.org/10.1007/s00209-014-1350-2

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