Global Melnikov theory in Hamiltonian systems with general time-dependent perturbations

DOI10.1007/s00332-018-9461-2zbMath1405.37065arXiv1710.01849OpenAlexW3099981103MaRDI QIDQ1631292

Marian Gidea, Rafael de la Llave

Publication date: 6 December 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.01849

zbMATH Keywords

perturbationArnold diffusionhomoclinic orbitsMelnikov theorymanifold splitting

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Perturbation theories for problems in Hamiltonian and Lagrangian mechanics (70H09) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items

Complex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillator, Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows, Analytic genericity of diffusing orbits in a priori unstable Hamiltonian systems, Arnold Diffusion in a Model of Dissipative System, A general mechanism of instability in Hamiltonian systems: skipping along a normally hyperbolic invariant manifold, Global effect of non-conservative perturbations on homoclinic orbits, Melnikov method for non-conservative perturbations of the restricted three-body problem

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