Reduction of secular error in approximations to harmonic oscillator systems with nonlinear perturbations

DOI10.1016/S0167-2789(98)00007-4zbMath1194.70034MaRDI QIDQ992192

Peter B. Kahn, Yair Zarmi

Publication date: 11 September 2010

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

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Forced motions for nonlinear problems in mechanics (70K40) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

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Cites Work

• Unique normal forms for vector fields and Hamiltonians
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The Hamiltonian Hopf bifurcation
• Minimal normal forms in harmonic oscillations with small nonlinear perturbations
• Freedom in minimal normal forms
• Uniqueness and non-uniqueness of normal forms for vector fields
• Nonlinear Propagation of Wave-Packets on Fluid Interfaces
• Perturbation methods and non-linear hyperbolic waves
• Freedom in small parameter expansion for nonlinear perturbations
• Radius renormalization in limit cycles
• Comparison of the Modified Method of Averaging and the Two Variable Expansion Procedure
• Higher Order Averaging and Related Methods for Perturbed Periodic and Quasi-Periodic Systems
• Averaging methods in nonlinear dynamical systems
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