Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems |
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Authors: | Peter E Kloeden Pedro Marín-Rubio |
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Institution: | 1.Institut für Mathematik,Johann Wolfgang Goethe Universit?t,Frankfurt am Main,Germany;2.Departamento de Ecuaciones Diferenciales y Análisis Numérico,Universidad de Sevilla,Sevilla,Spain |
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Abstract: | 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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Keywords: | |
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