Chaotic Dynamics in Nonautonomous Maps: Application to the Nonautonomous Hénon Map

Francisco Balibrea Iniesta, Carlos Lopesino, Stephen R Wiggins, Ana M Mancho

Research output: Contribution to journalArticle (Academic Journal)peer-review

8 Citations (Scopus)
263 Downloads (Pure)


In this paper, we analyze chaotic dynamics for two-dimensional nonautonomous maps through the use of a nonautonomous version of the Conley–Moser conditions given previously. With this approach we are able to give a precise definition of what is meant by a chaotic invariant set for nonautonomous maps. We extend the nonautonomous Conley–Moser conditions by deriving a new sufficient condition for the nonautonomous chaotic invariant set to be hyperbolic. We consider the specific example of a nonautonomous Hénon map and give sufficient conditions, in terms of the parameters defining the map, for the nonautonomous Hénon map to have a hyperbolic chaotic invariant set.
Original languageEnglish
Article number1550172
Number of pages14
JournalInternational Journal of Bifurcation and Chaos
Issue number12
Publication statusPublished - 15 Dec 2015


  • Chaotic dynamics
  • invariant set
  • hyperbolic


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