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Le Calvez, Patrice and Romero Ruiz del Portal, Francisco and Salazar, J. M. (2010) Indices of the iterates of R3homeomorphisms at fixed points which are isolated invariant sets. Journal of the london mathematical societysecond series, 82 (3). pp. 683696. ISSN 00246107

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Official URL: http://jlms.oxfordjournals.org/content/82/3/683.full.pdf
Abstract
Let U subset of R3 be an open set and f : U > f(U) subset of R3 be a homeomorphism. Let p is an element of U be a fixed point. It is known that if {p} is not an isolated invariant set, then the sequence of the fixedpoint indices of the iterates of f at p, (i(f(n), p))(n >=) (1), is, in general, unbounded. The main goal of this paper is to show that when {p} is an isolated invariant set, the sequence (i(f(n), p))(n >= 1) is periodic. Conversely, we show that, for any periodic sequence of integers (In)(n >= 1) satisfying Dold's necessary congruences, there exists an orientationpreserving homeomorphism such that i(f(n), p) = In for every n >= 1. Finally we also present an application to the study of the local structure of the stable/unstable sets at p.
Item Type:  Article 

Additional Information:  Dedicated to Professor Jose M. Montesinos on the occasion of his 65th birthday 
Uncontrolled Keywords:  Fixed point index; Dold’s congruences; Conley index; homeomorphism 
Subjects:  Sciences > Mathematics > Differential equations Sciences > Mathematics > Topology 
ID Code:  18099 
Deposited On:  31 Jan 2013 09:46 
Last Modified:  19 Feb 2019 11:58 
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