Transversal homoclinic points of a class of conservative diffeomorphisms

DOI10.1016/0022-0396(90)90012-EzbMath0717.58044MaRDI QIDQ2638631

Ernest Fontich

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

zbMATH Keywords

invariant manifoldsHénon maphomoclinic pointstandard mapheteroclinic point

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (18)

A note on homoclinic or heteroclinic orbits for the generalized Hénon map ⋮ Existence of analytic invariant curves for a complex planar mapping near resonance ⋮ Decreasing solutions and convex solutions of the polynomial-like iterative equation ⋮ Homoclinic points in the composition of two reflections ⋮ On cyclicity-one elliptic islands of the standard map ⋮ The polynomial-like iterative equation for PM functions ⋮ Continuously decreasing solutions for polynomial-like iterative equations ⋮ Topological entropy of standard type monotone twist maps ⋮ Smoothness ofO(N)-equivariant solutions of a polynomial-like iterative equation onR^N ⋮ Global solutions for leading coefficient problem of a general iterative equation ⋮ The essential coexistence phenomenon in dynamics ⋮ Leading coefficient problem for polynomial-like iterative equations ⋮ Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations ⋮ Transversal homoclinic points of the Hénon map ⋮ Existence of continuous solutions and stability for a general iterative functional equation ⋮ On series-like iterative equation with a general boundary restriction ⋮ Homoclinic shadowing ⋮ Analytic invariant curves for a planar map.

Cites Work

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• Homoclinic bifurcations and the area-conserving Henon mapping
• Chaotic behavior in the Henon mapping
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A two-dimensional mapping with a strange attractor
• Existence of a homoclinic point for the Henon map
• Stable and Random Motions in Dynamical Systems
• Computing the dependence on a parameter of a family of unstable manifolds: generalized Melnikov formulas
• Homoclinic Points of Area Preserving Diffeomorphisms
• Reversible Diffeomorphisms and Flows
• Numerical study of quadratic area-preserving mappings

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