Topological techniques for efficient rigorous computation in dynamics

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Abstract

We describe topological methods for the efficient, rigorous computation of dynamical systems. In particular, we indicate how Conley's Fundamental Decomposition Theorem is naturally related to combinatorial approximations of dynamical systems. Furthermore, we show that computations of Morse decompositions and isolating blocks can be performed efficiently. We conclude with examples indicating how these ideas can be applied to finite-and infinite-dimensional discrete and continuous dynamical systems.

Original languageEnglish (US)
Pages (from-to)435-477
Number of pages43
JournalActa Numerica
Volume11
DOIs
StatePublished - Jan 1 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Mathematics(all)

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