Simple scenarios of onset of chaos in three-dimensional maps

Alexander Gonchenko, Sergey Gonchenko, Alexey Kazakov, Dmitry Turaev

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


We give a qualitative description of two main routes to chaos in three-dimensional maps. We discuss Shilnikov scenario of transition to spiral chaos and a scenario of transition to discrete Lorenz-like and figure-eight strange attractors. The theory is illustrated by numerical analysis of three-dimensional Henon-like maps and Poincaré maps in models of nonholonomic mechanics.

Original languageEnglish
Article number1440005
JournalInternational Journal of Bifurcation and Chaos
Issue number8
StatePublished - 1 Jan 2014
Externally publishedYes


  • Celtic stone
  • Strange attractor
  • chaotic dynamics
  • homoclinic orbit
  • nonholonomic constraint
  • spiral attractor
  • three-dimensional Henon map
  • torus-chaos
  • unbalanced ball

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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