Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems

DOI10.1016/S0167-2789(97)00173-5zbMath0941.37021OpenAlexW2064274015MaRDI QIDQ1963422

Stephen Wiggins, Michael Rudnev

Publication date: 1 February 2000

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0167-2789(97)00173-5

zbMATH Keywords

KAM theoryArnold diffusionhomoclinic orbitsMelnikov integralsanalytic perturbationwhiskered toriexponentially small splitting of separatriceshomoclinic manifoldsa priori stable systemsNekhoroshev exponentweakly hyperbolic tori

Mathematics Subject Classification ID

Hamilton's equations (70H05) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Periodic and quasi-periodic flows and diffeomorphisms (37C55) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

MEL'NIKOV'S APPROXIMATION DOMINANCE: SOME EXAMPLES ⋮ Semi-analytic computations of the speed of Arnold diffusion along single resonances in a priori stable Hamiltonian systems ⋮ Continuation of the exponentially small transversality for the splitting of separatrices to a whiskered torus with silver ratio ⋮ On homoclinic splitting problems ⋮ Dynamics around simple resonant tori in nearly integrable Hamiltonian systems ⋮ A new method for measuring the splitting of invariant manifolds ⋮ On the ``hidden harmonics associated to best approximants due to quasi-periodicity in splitting phenomena ⋮ A functional analysis approach to Arnold diffusion ⋮ Exponentially Small Splitting of Separatrices and Transversality Associated to Whiskered Tori with Quadratic Frequency Ratio ⋮ Arnold diffusion in perturbations of analytic exact symplectic maps ⋮ Erratum to ``Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems ⋮ Geometrical approach to the splitting of separatrix for standard-like mappings

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