Infinite series in cohomology: attractors and the Conley index
We study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps f : U ⊆ Rd → Rd by analyzing the topological structure of their unstable manifold. We provide a simple dynamical interpretation for the first cohomological Conley index. A number of consequences are...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/133326 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/133326 |
| Access Level: | acceso abierto |
| Palabra clave: | Alexander–Spanier cohomology Attractors Conley index Fixed point index Index pairs Topología 1210.13 Dinámica Topológica |
| Sumario: | We study the cohomological Conley index of arbitrary isolated invariant continua for continuous maps f : U ⊆ Rd → Rd by analyzing the topological structure of their unstable manifold. We provide a simple dynamical interpretation for the first cohomological Conley index. A number of consequences are derived, including new computations of the fixed point indices of isolated invariant continua in dimensions 2 and 3. To obtain these results we develop a new method that may be of independent interest and involves the summation of power series in cohomology. |
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