Homoclinic twisting bifurcations and cusp horseshoe maps

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38 Scopus citations


Chaotic dynamics arises when the unstable manifold of a hyperbolic equilibrium point changes its twist type along a homoclinic orbit as some generic parameter is varied. Such bifurcation points occur naturally in singularly perturbed systems. Some quotient symbolic systems induced from the Bernoulli symbolic system on two symbols are proved to be characteristic for this new mechanism of chaos generation. Combination of geometrical and analytical methods is proved to be more fruitful.

Original languageEnglish (US)
Pages (from-to)417-467
Number of pages51
JournalJournal of Dynamics and Differential Equations
Issue number3
Publication statusPublished - Jul 1 1993



  • AMS classifications (1980): 00A71, 34A34, 34C28, 34D30, 58F12, 58F13, 58F14, 58F40
  • Strong inclination property
  • cusp horseshoe maps
  • neutrally twisted homoclinic orbits
  • quotient symbolic systems
  • singular perturbations

ASJC Scopus subject areas

  • Analysis

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