A shadowing approach to passage through resonance

DOI10.1017/S0308210500031358zbMath0722.34040MaRDI QIDQ3209451

James A. Murdock

Publication date: 1990

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

approximationscylindershadowing methodspassage through resonance

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Perturbations of ordinary differential equations (34D10) 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)

Related Items

Validity of the multiple scale method for very long intervals ⋮ Some foundational issues in multiple scale theory

Cites Work

• On the length of validity of averaging and the uniform approximation of elbow orbits, with an application to delayed passage through resonance
• Qualitative dynamics from asymptotic expansions: Local theory
• Perturbation Techniques for Oscillatory Systems with Slowly Varying Coefficients
• On the Passage through Resonance
• Averaging methods in nonlinear dynamical systems