Homoclinic and heteroclinic behavior in an infinite-degree-of-freedom Hamiltonian system: Chaotic free vibrations of an undamped, buckled beam

DOI10.1016/S0375-9601(01)00324-3zbMath0969.70509MaRDI QIDQ5936283

Kazuyuki Yagasaki

Publication date: 10 July 2001

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

orbitsinvariant torinonintegrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics (74H10) Dynamical systems in classical and celestial mechanics (37N05) Nonintegrable systems for problems in Hamiltonian and Lagrangian mechanics (70H07)

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Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Normally hyperbolic invariant manifolds in dynamical systems
• Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
• Horseshoes in two-degree-of-freedom Hamiltonian systems with saddle-centers
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Homoclinic and heteroclinic orbits to invariant tori in multi-degree-of-freedom Hamiltonian systems with saddle-centres
• Stable and Random Motions in Dynamical Systems
• A magnetoelastic strange attractor
• FAMILIES OF TRANSVERSE POINCARÉ HOMOCLINIC ORBITS IN 2N-DIMENSIONAL HAMILTONIAN SYSTEMS CLOSE TO THE SYSTEM WITH A LOOP TO A SADDLE-CENTER
• Differentiable invariant manifolds for partially hyperbolic tori and a lambda lemma
• Nonlinear Vibrations of a Buckled Beam Under Harmonic Excitation
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem