Asymptotically autonomous semiflows: Chain recurrence and lyapunov functions

Konstantin Mischaikow, Hal Smith, Horst Thieme

Research output: Contribution to journalArticle

155 Scopus citations

Abstract

From the work of C. Conley, it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set. Here, we improve a result of L. Markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow. In the special case that there is a Lyapunov function for the limiting semiflow, sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the Lyapunov function.

Original languageEnglish (US)
Pages (from-to)1669-1685
Number of pages17
JournalTransactions of the American Mathematical Society
Volume347
Issue number5
DOIs
StatePublished - May 1995

Keywords

  • Asymptotically autonomous semiflow
  • Chain recurrence
  • Lyapunov function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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