Open Access

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

Fixed Point Theory and Applications20102010:323069

DOI: 10.1155/2010/323069

Received: 11 November 2009

Accepted: 1 March 2010

Published: 18 May 2010

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’ Affiliations

(1)
Departamento de Geometría y Topología, Facultad de CC.Matemáticas, Universidad Complutense de Madrid
(2)
Departamento de Matemáticas, Universidad de Alcalá

Copyright

© F. R. Ruiz del Portal and J. M. Salazar. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.