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Local fixed point indices of iterations of planar maps


Romero Ruiz del Portal, Francisco y Graff, Grzegorz y Nowak-Przygodzki, Piotr (2011) Local fixed point indices of iterations of planar maps. Journal of Dynamics and Differential Equations, 23 (1). pp. 213-223. ISSN 1040-7294

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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

Tipo de documento:Artículo
Palabras clave:Fixed point index; Conley index, Nielsen number; Periodic points; Iterations
Materias:Ciencias > Matemáticas > Topología
Código ID:13994

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