Negatively Invariant Sets and Entire Solutions |
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Authors: | Peter E Kloeden Pedro Marín-Rubio |
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Institution: | 1. Institut für Mathematik, Goethe Universit?t, 60054, Frankfurt am Main, Germany 2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080, Sevilla, Spain
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Abstract: | Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated
in terms of processes, are shown to contain a strictly invariant set and hence entire solutions. For completeness the positively
invariant case is also considered. Both discrete and continuous time systems are considered. In the nonautonomous case, the
various types of invariant sets are in fact families of subsets of the state space that are mapped onto each other by the
process. A simple example shows the usefulness of the result for showing the occurrence of a bifurcation in a nonautonomous
system. |
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Keywords: | |
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