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A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms

Fixed Point Theory and Applications volume 2010, Article number: 323069 (2010) Cite this article

Abstract

Let be an open subset and be an arbitrary local homeomorphism with . We compute the fixed point indices of the iterates of at , and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincaré index formula without differentiability assumptions. Our techniques apply equally to both orientation preserving and orientation reversing homeomorphisms. We present some new results, especially in the orientation reversing case.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de CC.Matemáticas, Universidad Complutense de Madrid, Madrid, 28040, Spain

    FranciscoR Ruiz del Portal

  2. Departamento de Matemáticas, Universidad de Alcalá, Alcalá de Henares, Madrid, 28871, Spain

    JoséM Salazar

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  1. FranciscoR Ruiz del Portal
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  2. JoséM Salazar
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Correspondence to FranciscoR Ruiz del Portal.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Ruiz del Portal, F., Salazar, J. A Poincaré Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms. Fixed Point Theory Appl 2010, 323069 (2010). https://doi.org/10.1155/2010/323069

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  • DOI: https://doi.org/10.1155/2010/323069

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