Homoclinic twisting bifurcations and cusp horseshoe maps

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

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
Volume5
Issue number3
DOIs
StatePublished - Jul 1 1993

Fingerprint

Homoclinic Bifurcation
Horseshoe
Cusp
Unstable Manifold
Singularly Perturbed Systems
Homoclinic Orbit
Bifurcation Point
Chaotic Dynamics
Analytical Methods
Bernoulli
Equilibrium Point
Twist
Chaos
Quotient

Keywords

  • 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

Cite this

Homoclinic twisting bifurcations and cusp horseshoe maps. / Deng, Bo.

In: Journal of Dynamics and Differential Equations, Vol. 5, No. 3, 01.07.1993, p. 417-467.

Research output: Contribution to journalArticle

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