Fixed point index in hyperspaces: A Conley-type index for discrete semidynamical systems
Let X be a locally compact metric absolute neighbourhood retract for metric spaces, UX 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, KU, this fixed p...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2001 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/57115 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57115 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.1 Fixed point index Hyperspaces Attractors Topología 1210 Topología |
| Sumario: | Let X be a locally compact metric absolute neighbourhood retract for metric spaces, UX 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, KU, 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. |
|---|