scholarly journals The lie transform: A new approach to classical perturbation theory

1978 ◽  
Author(s):  
Allan N. Kaufman
Keyword(s):  
Perturbation Theory ◽  
New Approach ◽  
Lie Transform ◽  
Classical Perturbation Theory

New Approach to Perturbation Theory.

1979 ◽  
Vol 43 (2) ◽  
pp. 176-176 ◽  
Author(s):  
Y. Aharonov ◽  
C. K. Au
Keyword(s):  
Perturbation Theory ◽  
New Approach

Global Behavior of a Nonlinear Quasiperiodic Mathieu Equation

2001 ◽  
Author(s):  
Randolph S. Zounes ◽  
Richard H. Rand
Keyword(s):  
Perturbation Theory ◽  
Nonlinear Term ◽  
Mathieu Equation ◽  
Elliptic Functions ◽  
Action Space ◽  
Global Behavior ◽  
Trigonometric Functions ◽  
Lie Transform ◽  
Analytic Expressions ◽  
Subharmonic Resonances

Abstract We investigate the interaction of subharmonic resonances in the nonlinear quasiperiodic Mathieu equation,(1)x..+[δ+ϵ(cos⁡ω1t+cos⁡ω2t)]x+αx3=0. We assume that ϵ ≪ 1 and that the coefficient of the nonlinear term, α, is positive but not necessarily small. We utilize Lie transform perturbation theory with elliptic functions — rather than the usual trigonometric functions — to study subharmonic resonances associated with orbits in 2m : 1 resonance with a respective driver. In particular, we derive analytic expressions that place conditions on (δ, ϵ, ω1, ω2) at which subharmonic resonance bands in a Poincaré section of action space begin to overlap. These results are used in combination with Chirikov’s overlap criterion to obtain an overview of the O(ϵ) global behavior of equation (1) as a function of δ and ω2 with ω1, α, and ϵ fixed.

Simulation of Multifrequency EPR Spectra from Mn(III)/Mn(IV) Catalase of Lactobacillus plantarum Using a New Approach Based on Perturbation Theory

1994 ◽  
Vol 33 (12) ◽  
pp. 2677-2682 ◽  
Author(s):  
Alice Haddy ◽  
Geoffrey S. Waldo ◽  
Richard H. Sands ◽  
James E. Penner-Hahn
Keyword(s):  
Perturbation Theory ◽  
Lactobacillus Plantarum ◽  
Epr Spectra ◽  
New Approach
Sign in / Sign up

Export Citation Format

Share Document