Asymptotic Formulae for Dynamic Characteristics of a Particle in the Vicinity of Resonance

M. A. Guzev

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok

Abstract: Asymptotic formulae for the action-angle variables are constructed for low and high-energy particles in the vicinity of a nonlinear resonance. Estimation of the approximation accuracy with respect to the energy parameter and some characteristics of the model Hamiltonian are obtained.

Key words: nonlinear dynamics, nonlinear resonance, Lennard — Jones potential, asymptotic behavior.

UDC: 551.465.7

MSC: 35B38

Received: 06.07.2012