Nondegenerate homoclinic tangency and hyperbolic sets

DOI10.1016/S0362-546X(02)00271-7zbMath1023.37012OpenAlexW2026104157MaRDI QIDQ1863619

Ming-Chia Li

Publication date: 11 March 2003

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(02)00271-7

zbMATH Keywords

Hénon mapsurface diffeomorphismcone fielddissipative periodic saddle pointnondegenerate homoclinic tangencyuniform and nonuniformly hyperbolic sets

Mathematics Subject Classification ID

Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems with hyperbolic orbits and sets (37D05) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Cites Work

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• The dynamics of the Hénon map
• Bifurcation to infinitely many sinks
• A two-dimensional mapping with a strange attractor
• Unfolding homoclinic tangencies inside horseshoes: hyperbolicity, fractal dimensions and persistent tangencies
• THE PALIS AND TAKENS’ PROBLEM ON THE FIRST HOMOCLINIC TANGENCY INSIDE THE HORSESHOE
• Hyperbolicity of a special one-parameter family with a first homoclinic tangency
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I

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