Adiabatic variation. I: Exponential property for the simple oscillator

DOI10.1007/BF01595197zbMath0268.41014MaRDI QIDQ758656

Richard E. Meyer

Publication date: 1973

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

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Linear ordinary differential equations and systems (34A30) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Dynamical systems and ergodic theory (37-XX)

Related Items (9)

Reflection coefficient beyond all orders for singular problems. I: Separated critical points on the nearest critical level line ⋮ Transcendentally small reflection of waves for problems with/without turning points near infinity: A new uniform approach ⋮ Exponential asymptotics and adiabatic invariance of a simple oscillator ⋮ Adiabatic variation. II: Action change for the simple oscillator ⋮ Energy evolution in the time-dependent harmonic oscillator with arbitrary external forcing ⋮ The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance ⋮ Adiabatic variation. III: A deep mirror model ⋮ Adiabatic variation. IV: Action change of a pendulum for general frequency ⋮ Energy Evolution in Time-Dependent Harmonic Oscillator

Cites Work

• Lorentz's pendulum problem
• Fourier Transforms and the Method of Stationary Phase
• Unnamed Item

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