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

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 wit...

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Detalles Bibliográficos
Autores: Romero Ruiz del Portal, Francisco, Salazar, J. M.
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/42536
Acceso en línea:https://hdl.handle.net/20.500.14352/42536
Access Level:acceso abierto
Palabra clave:517.9
515.1
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Descripción
Sumario: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.