MULTIPLIERS OF HOMOCLINIC TANGENCIES AND A THEOREM OF GONCHENKO AND SHILNIKOV ON AREA PRESERVING MAPS

DOI10.1142/S0218127405014246zbMath1128.37032OpenAlexW2019669462MaRDI QIDQ5474367

Todd R. Young, Valentin Afraimovich

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405014246

zbMATH Keywords

hyperbolic fixed-point

Mathematics Subject Classification ID

Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Cites Work

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• Lorenz type attractors from codimension one bifurcation
• A geometric criterion for positive topological entropy. II: Homoclinic tangencies
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Conventional multipliers for homoclinic orbits
• Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits