Horseshoes for autonomous Hamiltonian systems using the Melnikov integral

DOI10.1017/S0143385700009500zbMath0666.58039OpenAlexW1969424657MaRDI QIDQ3817344

Clark Robinson

Publication date: 1988

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700009500

zbMATH Keywords

Hamiltonian systemshyperbolic fixed pointautonomous perturbationshyperbolic closed orbits

Mathematics Subject Classification ID

Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40)

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Cites Work

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• Bifurcation to infinitely many sinks
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Pathology in dynamical systems. III: Analytic Hamiltonians
• Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
• Moser's implicit function theorem in the framework of analytic smoothing
• Homoclinic orbits in Hamiltonian systems
• Diffeomorphisms with infinitely many sinks
• Convergent series expansions for quasi-periodic motions
• Ω-Stable Limit Set Explosions
• The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
• Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I

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