Averaging, passage through resonances, and capture into resonance in two-frequency systems

DOI10.1070/RM2014v069n05ABEH004917zbMath1319.34073OpenAlexW2004702712MaRDI QIDQ5244952

Anatoly I. Neishtadt

Publication date: 1 April 2015

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rm2014v069n05abeh004917

zbMATH Keywords

resonanceaveraging method

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Motion of charged particles (78A35) Adiabatic invariants for problems in Hamiltonian and Lagrangian mechanics (70H11) Resonance phenomena for ordinary differential equations involving randomness (34F15) Averaging of perturbations for nonlinear problems in mechanics (70K65)

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Geometry of slow-fast Hamiltonian systems and Painlevé equations ⋮ Painlevé II equation as a model of a resonant interaction of oscillators ⋮ Capture and keeping of a resonance near equilibrium ⋮ On the topology of nearly-integrable Hamiltonians at simple resonances ⋮ Near-resonances and detuning in classical and quantum mechanics ⋮ Charged particle nonlinear resonance with localized electrostatic wave-packets ⋮ On the measure of KAM tori in two degrees of freedom ⋮ Capture and holding of resonance far from equilibrium ⋮ Two-Frequency Averaging in the Problem of Motion of a Counter-Rotating Vertical Axis Wind Turbine ⋮ On the frequency of a nonlinear oscillator ⋮ Passages through resonances in classical dynamics of a driven hydrogen atom ⋮ Resonance capture in a system of two oscillators near equilibrium

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