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Fixed point index and decompositions of planar invariant compacta

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Romero Ruiz del Portal, Francisco and Salazar, J. M. (2004) Fixed point index and decompositions of planar invariant compacta. Topology and its Applications, 141 (1-3). pp. 207-223. ISSN 0166-8641

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Official URL: http://www.sciencedirect.com/science/journal/01668641


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Abstract

Let U c R2 be an open subset and let f :U → f (U) c R2 be a homeomorphism. Let M = M1 U· · ·U Mr C U be a disjoint union of discs that isolates the invariant compactum K. The aimof this paper is to study the dynamics of f in K and to use the fixed point index to detect, in a simple and geometric way, the existence of periodic orbits on which f follows a determined pattern. Our method allows us to compute the fixed point index of every iteration of f in a neighborhood of the periodic orbits following a given itinerary in classical and important semidynamical systems with chaotic dynamics.


Item Type:Article
Uncontrolled Keywords:Fixed point index; Conley index; Filtration pairs
Subjects:Sciences > Mathematics > Topology
ID Code:19875
Deposited On:11 Feb 2013 15:28
Last Modified:12 Dec 2018 15:13

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