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Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems

Romero Ruiz del Portal, Francisco and Salazar, J. M. (2001) Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems. Journal London Mathematical Society, 64 (1). pp. 191-204. ISSN 1469-7750

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Abstract

Let X be a locally compact metric absolute neighbourhood retract for metric spaces, UX be an open subset and f :U→X be a continuous map. The aim of the paper is to study the fixed point index of the map that f induces in the y perspace of X. For any compact isolated invariant set, KU, this fixed point index produces, in a very natural way, a Conley-type (integer valued) index for K. This index is computed and it is shown that it only depends on what is called the attracting part of K. The index is used to obtain a characterization of isolating neighbourhoods of compact invariant sets with non-empty attracting part. This index also provides a characterization of compact isolated minimal sets that are attractors.


Item Type:Article
Uncontrolled Keywords:Fixed point index; Hyperspaces; Attractors
Subjects:Sciences > Mathematics > Topology
ID Code:13970
Deposited On:28 Nov 2011 11:26
Last Modified:28 Nov 2011 11:26

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