Random and deterministic perturbations of nonlinear oscillators
type: Item
instance of: scholarly article
title: Random and deterministic perturbations of nonlinear oscillators
zbMATH Open document ID: 0908.60051
author: Mark Freidlin
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/227564
full work available at URL: Freidlin.MAN.html
review text: Perturbations of Hamiltonian systems are considered: \[ \dot p_t^\varepsilon= -f(q_t^\varepsilon)+\varepsilon\beta(p^\varepsilon_t,q^\varepsilon_t) +\sqrt{\varepsilon}\sigma(p^\varepsilon_t,q^\varepsilon_t)\circ\dot W_t,\qquad \dot q^\varepsilon_t=p^\varepsilon_t. \] The long-time behaviour is governed by a stochastic process on a graph related to the Hamiltonian system. The characteristics of the process for systems with one degree of freedom are calculated.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 35B20
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 34F05
zbMATH DE Number: 1184362
zbMATH Keywords: random perturbations
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: partial differential equations
zbMATH Keywords: small parameter
reviewed by: Marek Capiński
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184362