Lattice Structures for Attractors II

William D. Kalies, Konstantin Mischaikow, Robert C.A. M Vandervorst

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The algebraic structure of the attractors in a dynamical system determines much of its global dynamics. The collection of all attractors has a natural lattice structure, and this structure can be detected through attracting neighborhoods, which can in principle be computed. Indeed, there has been much recent work on developing and implementing general computational algorithms for global dynamics, which are capable of computing attracting neighborhoods efficiently. Here we address the question of whether all of the algebraic structure of attractors can be captured by these methods.

Original languageEnglish (US)
Pages (from-to)1151-1191
Number of pages41
JournalFoundations of Computational Mathematics
Volume16
Issue number5
DOIs
StatePublished - Oct 1 2016

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All Science Journal Classification (ASJC) codes

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

Keywords

  • Attracting neighborhood
  • Attractor
  • Birkhoff’s representation theorem
  • Distributive lattice
  • Invariant set

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