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

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Romero Ruiz del Portal, Francisco and Salazar, J. M. (2010) A Poincare Formula for the Fixed Point Indices of the Iterates of Arbitrary Planar Homeomorphisms. Fixed Point Theory and Applications . 31 Pg.. ISSN 1687-1820

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Official URL: http://www.emis.de/journals/HOA/FPTA/Volume2010/323069.pdf



Abstract

Let U subset of R(2) be an open subset and f : U -> R(2) be an arbitrary local homeomorphism with Fix(f) = {p}. We compute the fixed point indices of the iterates of f at p, i(R2)(f(k), p), and we identify these indices in dynamical terms. Therefore, we obtain a sort of Poincare 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.


Item Type:Article
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Dedicated to professor José M. Montesinos in the occasion of his 65th birthday and to the memory of professor Julián Martínez.

Subjects:Sciences > Mathematics > Differential equations
Sciences > Mathematics > Topology
ID Code:18100
Deposited On:01 Feb 2013 12:28
Last Modified:12 Dec 2018 15:13

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