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Local fixed point indices of iterations of planar maps

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Romero Ruiz del Portal, Francisco and Graff, Grzegorz and 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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Official URL: http://www.springerlink.com/openurl.asp?genre=journalissn=1040-7294



Abstract

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.


Item Type:Article
Uncontrolled Keywords:Fixed point index; Conley index, Nielsen number; Periodic points; Iterations
Subjects:Sciences > Mathematics > Topology
ID Code:13994
Deposited On:07 Dec 2011 09:12
Last Modified:12 Dec 2018 15:13

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