A completion construction for continuous dynamical systems
- García Calcines, J.M. 1
- Hernández Paricio, L.J. 2
- Rivas Rodríguez, M.T. 2
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1
Universidad de La Laguna
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2
Universidad de La Rioja
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ISSN: 1230-3429
Year of publication: 2014
Volume: 44
Issue: 2
Pages: 497-526
Type: Article
More publications in: Topological Methods in Nonlinear Analysis
Abstract
In this work we use the theory of exterior spaces to construct a (Formula Presented)-completion and a (Formula Presented)-completion of a dynamical system. If X is a flow, we construct canonical maps (Formula Presented) and (Formula Presented) and when these maps are homeomorphisms we have the class of (Formula Presented)-complete and (Formula Presented) -complete flows, respectively. In this study we find out many relations between the topological properties of the completions and the dynamical properties of a given flow. In the case of a complete flow this gives interesting relations between the topological properties (separability properties, compactness, convergence of nets, etc.) and dynamical properties (periodic points, omega limits, attractors, repulsors, etc.).