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

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• 作者：Peter E. Kloeden (1) kloeden@math.uni-frankfurt.de
  Pedro Mar铆n-Rubio (2) pmr@us.es
• 关键词：Entire solutions &#8211 ; Invariant sets &#8211 ; Positively invariant sets &#8211 ; Negatively invariant sets &#8211 ; Set ; valued dynamical systems &#8211 ; Autonomous and nonautonomous dynamical systems &#8211 ; Set ; valued processes
• 刊名：Set-Valued and Variational Analysis
• 出版时间：March 2011
• 出版年：2011
• 期刊代码：113_09276947
• 类别：bio
• 卷：19
• 期：1
• 页码：43-57
• 数据来源：sp

摘要

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.