Homoclinic twisting bifurcations and cusp horseshoe maps

Bo Deng

doi:10.1007/BF01053531

Homoclinic twisting bifurcations and cusp horseshoe maps

Bo Deng

Mathematics

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

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 language	English (US)
Pages (from-to)	417-467
Number of pages	51
Journal	Journal of Dynamics and Differential Equations
Volume	5
Issue number	3
DOIs	https://doi.org/10.1007/BF01053531
State	Published - Jul 1993

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

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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.",

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AB - 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.

KW - AMS classifications (1980): 00A71, 34A34, 34C28, 34D30, 58F12, 58F13, 58F14, 58F40

KW - Strong inclination property

KW - cusp horseshoe maps

KW - neutrally twisted homoclinic orbits

KW - quotient symbolic systems

KW - singular perturbations

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Homoclinic twisting bifurcations and cusp horseshoe maps

Abstract

Keywords

ASJC Scopus subject areas

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