Examples of lorenz-like attractors in hénon-like maps

S. V. Gonchenko, A. S. Gonchenko, I. I. Ovsyannikov, D. V. Turaev

Research output: Contribution to journalArticlepeer-review

29 Scopus citations

Abstract

We display a gallery of Lorenz-like attractors that emerge in a class of three-dimensional maps. We review the theory of Lorenz-like attractors for diffeomorphisms (as opposed to flows), define various types of such attractors, and find sufficient conditions for three-dimensional Henon-like maps to possess pseudohyperbolic Lorenz-like attractors. The numerically obtained scenarios of the creation and destruction of these attractors are also presented.

Original languageEnglish
Pages (from-to)48-70
Number of pages23
JournalMathematical Modelling of Natural Phenomena
Volume8
Issue number5
DOIs
StatePublished - 14 Oct 2013
Externally publishedYes

Keywords

  • Bifurcations
  • Homoclinic orbit
  • Homoclinic tangency
  • Normal form
  • Pseudohyperbolicity
  • Strange attractor
  • Three-dimensional maps
  • Volume hyperbolicity
  • Wild set

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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