Some duality properties of non-saddle sets
We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting-that the Conley index of a regular isolated non-saddle...
| Autores: | , , , |
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| 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:20.500.14352/57293 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/57293 |
| Access Level: | acceso abierto |
| Palabra clave: | 515.143 517.938 Dynamical system Isolated set Non-saddle set Shape Topología 1210 Topología |
| Sumario: | We show in this paper that the class of compacts that call be isolated non-saddle sets of flows in ANRs is precisely the class of compacta with polyhedral shape. We also prove-reinforcing the essential role played by shape theory in this setting-that the Conley index of a regular isolated non-saddle set is determined, in certain cases, by its shape. We finally introduce and study the notion of dual of a non-saddle set. Examples of compacta related by duality are attractor-repeller pairs. We use the complement theorems in shape theory to prove that the shape of the dual set is determined by the shape of the original non-saddle set. |
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