Studying discrete dynamical systems through differential equations

Anna Cima, Armengol Gasull, Víctor Mañosa

Research output: Contribution to journalArticleResearchpeer-review

18 Citations (Scopus)

Abstract

In this paper we consider dynamical systems generated by a diffeomorphism F defined on U an open subset of Rn, and give conditions over F which imply that their dynamics can be understood by studying the flow of an associated differential equation, over(x, ̇) = X (x), also defined on U. In particular the case where F has n - 1 functionally independent first integrals is considered. In this case X is constructed by imposing that it shares with F the same set of first integrals and that the functional equation μ (F (x)) = det (D F (x)) μ (x), x ∈ U, has some non-zero solution, μ. Several examples for n = 2, 3 are presented, most of them coming from several well-known difference equations. © 2007 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)630-648
JournalJournal of Differential Equations
Volume244
DOIs
Publication statusPublished - 1 Feb 2008

Keywords

  • Conjugation of flows
  • Difference equations
  • Integrable mappings
  • Integrable vector fields
  • Lie symmetries

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