Sigma map dynamics and bifurcations

Aminur Rahman, Yogesh Joshi, Denis Blackmore

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Some interesting variants of walking droplet based discrete dynamical bifurcations arising from diffeomorphisms are analyzed in detail. A notable feature of these new bifurcations is that, like Smale horseshoes, they can be represented by simple geometric paradigms, which markedly simplify their analysis. The two-dimensional diffeomorphisms that produce these bifurcations are called sigma maps or double sigma maps for reasons that are made manifest in this investigation. Several examples are presented along with their dynamical simulations.

Original languageEnglish (US)
Pages (from-to)740-749
Number of pages10
JournalRegular and Chaotic Dynamics
Volume22
Issue number6
DOIs
StatePublished - Nov 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Keywords

  • Discrete dynamical systems
  • bifurcations
  • chaotic strange attractors
  • dynamical crises
  • homoclinic and heteroclinic orbits
  • invariant sets
  • sigma maps

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