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Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems

 

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Author: Kloeden, Peter E.
Marín Rubio, Pedro
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2011
Published in: Journal of Dynamics and Differential Equations, 19 (1), 43-57
Document type: Article
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.
Cite: Kloeden, P.E. y Marín Rubio, P. (2011). Negatively Invariant Sets and Entire Trajectories of Set-Valued Dynamical Systems. Journal of Dynamics and Differential Equations, 19 (1), 43-57.
Size: 178.7Kb
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URI: http://hdl.handle.net/11441/25934

DOI: 10.1007/s11228-009-0123-2

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