Dynamics of a two-dimensional map on nested circles and rings

Fabio Tramontana, Laura Gardini, Iryna Sushko

Research output: Contribution to journalArticle

Abstract

We consider a discrete dynamical system, a two-dimensional real map which represents a one-dimensional complex map. Depending on the parameters, its bounded dynamics can be restricted to an invariant circle, cyclic invariant circles, invariant annular regions or disks. We show that on such invariant sets the trajectories are always either periodic of the same period, or quasiperiodic and dense. Moreover, the invariant sets may be transversely attracting or repelling, and undergo the typical cascade of period doubling bifurcations. Homoclinic bifurcations can also occur, leading to chaotic rings, annular regions filled with dense repelling cyclical circles and aperiodic trajectories.
Original languageEnglish
Pages (from-to)N/A-N/A
JournalChaos, Solitons and Fractals
Volume143
DOIs
Publication statusPublished - 2021

Keywords

  • Dynamics on nested circles and rings
  • Linear fractional maps
  • Non standard Neimark-Sacker bifurcation
  • Two-dimensional maps

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