Chaotic motions near homoclinic manifolds and resonant tori in quasiperiodic perturbations of planar Hamiltonian systems

DOI10.1016/0167-2789(93)90090-NzbMath0794.34037OpenAlexW1967211878MaRDI QIDQ1325883

Kazuyuki Yagasaki

Publication date: 5 June 1994

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

Full work available at URL: https://doi.org/10.1016/0167-2789(93)90090-n

zbMATH Keywords

nonlinear oscillatorschaotic dynamicshomoclinic orbitnumerical simulationBernoulli shiftsecond-order averaging methodplanar Hamiltonian systemquasiperiodically forced Duffing oscillatorfamily of invariant 3- torihomoclinic manifoldMelnikov's techniqueone-parameter family of periodic orbitstwo-frequency quasiperiodic perturbation

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Ordinary differential equations and systems on manifolds (34C40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Heteroclinic chaotic behavior driven by a Brownian motion ⋮ Frictional oscillations under the action of almost periodic excitation ⋮ Chaotic behavior in differential equations driven by a Brownian motion ⋮ Quasi-periodically forced nonlinear Helmholtz oscillators

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