Título: | Local fixed point indices of iterations of planar maps |
Autores: | Romero Ruiz del Portal, Francisco ; Graff, Grzegorz ; Nowak-Przygodzki, Piotr |
Tipo de documento: | texto impreso |
Editorial: | Springer, 2011 |
Dimensiones: | application/pdf |
Nota general: | info:eu-repo/semantics/openAccess |
Idiomas: | |
Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Topología , Tipo = Artículo |
Resumen: |
Let f : U ?R2 be a continuous map, where U is an open subset of R2. We consider a fixed point p of f which is neither a sink nor a source and such that ?p? is an isolated invariant set. Under these assumption we prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations ?ind(fn, p)? ?n=1 is periodic,bounded by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem [Annals of Math., 146 (1997), 241-293] onto the class of non-injective maps. We apply our result to study the dynamics of continuous maps on 2-dimensional sphere. |
En línea: | https://eprints.ucm.es/id/eprint/13994/1/localfixed.pdf |
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