Improved N-th order averaging theory for periodic systems

DOI10.1016/0022-0396(90)90083-2zbMath0704.34067OpenAlexW2064431160MaRDI QIDQ916858

H. Scott Dumas, Albert W. Sáenz, James A. Ellison

Publication date: 1990

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90083-2

zbMATH Keywords

small parameterperiodic perturbationsaveraging procedure

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Averaging method for ordinary differential equations (34C29) Growth and boundedness of solutions to ordinary differential equations (34C11) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items

Proof of the existence of the axial-to-planar channeling transition in a simple crystal model ⋮ Validity of the multiple scale method for very long intervals ⋮ Higher-order averaging for nonperiodic systems ⋮ Averaging methods for finding periodic orbits via Brouwer degree. ⋮ Dynamics of axial channeling in quasicrystals: An averaging-theory approach ⋮ A stochastic theory of adiabatic invariance ⋮ Tight estimates for general averaging applied to almost-periodic differential equations ⋮ Axial channeling in perfect crystals, the continuum model, and the method of averaging ⋮ Higher-order averaging: periodic solutions, linear systems and an application

Cites Work

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• Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
• New approach to the asymptotic theory of nonlinear oscillations and wave- propagation
• Formulae for high derivatives of composite functions
• A Reproductive Property for a Class of Non-Newtonian Fluids
• Higher Order Averaging and Related Methods for Perturbed Periodic and Quasi-Periodic Systems
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• Averaging methods in nonlinear dynamical systems

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