Melnikov's method, stochastic layers and nonintegrability of a perturbed Duffing-oscillator

DOI10.1216/rmjm/1181072709zbMath0770.34027OpenAlexW2038122007MaRDI QIDQ1209559

Lawrence M. Perko

Publication date: 16 May 1993

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072709

zbMATH Keywords

perturbation theoryhomoclinic orbitstochastic layersubharmonic resonanceDuffing nonlinear oscillatorMelnikov's functionsubharmonic periodic orbitstwo-degrees-of-freedom Hamiltonian dynamical system

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (1)

CHAOS IN THE REORIENTATION PROCESS OF A DUAL-SPIN SPACECRAFT WITH TIME-DEPENDENT MOMENTS OF INERTIA

Cites Work

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• Proof of non-integrability for the Hénon-Heiles Hamiltonian near an exceptional integrable case
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system
• Resonance bands in a two degree of freedom Hamiltonian system
• An example of bifurcation to homoclinic orbits
• Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
• Homoclinic points near elliptic fixed points

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