Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems
Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire solutions. For completeness the strongly positiv...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/25934 |
| Acesso em linha: | http://hdl.handle.net/11441/25934 https://doi.org/10.1007/s11228-009-0123-2 |
| Access Level: | acceso abierto |
| Palavra-chave: | Entire solutions Invariant sets Positively invariant sets Negatively invariant sets Set-valued dynamical systems Autonomous and nonautonomous dynamical systems Set-valued processes |
| Resumo: | Strongly negatively invariant compact sets of set-valued autonomous and nonautonomous dynamical systems on a complete metric space, the latter formulated in terms of processes, are shown to contain a weakly positively invariant family and hence entire solutions. For completeness the strongly positively invariant case is also considered, where the obtained invariant family is strongly invariant. Both discrete and continuous time systems are treated. In the nonautonomous case, the various types of invariant families are in fact composed of subsets of the state space that are mapped onto each other by the set-valued process. A simple example shows the usefulness of the result for showing the occurrence of a bifurcation in a set-valued dynamical system. |
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