An algorithmic approach to chain recurrence

W. D. Kalies, K. Mischaikow, R. C.A.M. VanderVorst

Research output: Contribution to journalArticle

57 Scopus citations

Abstract

In this paper we give a new definition of the chain recurrent set of a continuous map using finite spatial discretizations. This approach allows for an algorithmic construction of isolating blocks for the components of Morse decompositions which approximate the chain recurrent set arbitrarily closely as well as discrete approximations of Conley's Lyapunov function. This is a natural framework in which to develop computational techniques for the analysis of qualitative dynamics including rigorous computer-assisted proofs.

Original languageEnglish (US)
Pages (from-to)409-449
Number of pages41
JournalFoundations of Computational Mathematics
Volume5
Issue number4
DOIs
StatePublished - Nov 1 2005
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Keywords

  • Algorithms
  • Chain recurrence
  • Combinatorial dynamics
  • Computation
  • Conley's decomposition theorem
  • Lyapunov function

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