Long-time behavior of weakly coupled oscillators
type: Item
instance of: scholarly article
title: Long-time behavior of weakly coupled oscillators
zbMATH Open document ID: 1119.34044
published in: Journal of Statistical Physics
publication date: 2006-11-27T00:00:00Z
review text: The authors consider small perturbations of a simple completely integrable system with many degree of freedoms, that is called weakly coupled oscillators. They investigated the long-time behavior of the perturbed system, in particular, its slow motion part, which means the deviations from non-perturbed trajectories, within an appropriate time scale, and show that the limit behavior of slow motion is described as Markov process on the space associated with first integral of the non-perturbed system. The behavior of two weakly coupled oscillators is illustrated as an example.
Mathematics Subject Classification ID: 34E10
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 5076312
zbMATH Keywords: Hamiltonian system
author: Mark Freidlin
author: Alexander D. Wentzell
reviewed by: Makiko Nisio
MaRDI profile type: Publication
full work available at URL: s10955-006-9133-8
OpenAlex ID: W2021144837
cites work: On stochastic behavior of perturbed Hamiltonian systems
cites work: Random perturbations of Hamiltonian systems
cites work: Q4225410
cites work: Averaging Principle for Stochastic Perturbations of Multifrequency Systems
cites work: Diffusion processes on an open book and the averaging principle
cites work: Multiphase averaging for classical systems. With applications to adiabatic theorems. Transl. from the French by H. S. Dumas
cites work: Q3862204
DOI: 10.1007/S10955-006-9133-8
description: scientific article; zbMATH DE number 5076312