On the length of validity of averaging and the uniform approximation of elbow orbits, with an application to delayed passage through resonance

DOI10.1007/BF00948965zbMath0671.34014OpenAlexW2094415036MaRDI QIDQ1119794

James A. Murdock

Publication date: 1988

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00948965

zbMATH Keywords

resonanceMorse-Smalehyperbolic periodic solutionelbow orbit

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theoretical approximation of solutions to ordinary differential equations (34A45)

Related Items (3)

Validity of the multiple scale method for very long intervals ⋮ A shadowing approach to passage through resonance ⋮ Some foundational issues in multiple scale theory

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Qualitative dynamics from asymptotic expansions: Local theory
• Some Asymptotic Estimates for Higher Order Averaging and a Comparison with Iterated Averaging
• Melnikov’s Method at a Saddle-Node and the Dynamics of the Forced Josephson Junction
• On the Passage through Resonance
• On a Derivative-Expansion Technique and Some Comments on Multiple Scaling in the Asymptotic Approximation of Solutions of Certain Differential Equations
• On a common derivation of the averaging method and the two-timescale method
• Averaging methods in nonlinear dynamical systems

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