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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 Society. Second Series, 82 (2). pp. 683696. ISSN 00246107

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Official URL: http://jlms.oxfordjournals.org/content/82/3/683.full.pdf+html
Abstract
Let U ⊂ R3 be an open set and f : U → f(U) ⊂ R3 be a homeomorphism. Let p ∈ 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(fn, p))n1, is, in general, unbounded. The main goal
of this paper is to show that when {p} is an isolated invariant set, the sequence (i(fn, p))n1 is periodic. Conversely, we show that, for any periodic sequence of integers (In)n1 satisfying Dold’s necessary congruences, there exists an orientationpreserving homeomorphism such that i(fn, 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 
Subjects:  Sciences > Mathematics > Differential equations Sciences > Mathematics > Topology 
ID Code:  18167 
Deposited On:  07 Feb 2013 11:24 
Last Modified:  20 Feb 2019 10:25 
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