Exponential stability of an invariant torus of a nonlinear countable system of differential equations
type: Item
instance of: scholarly article
title: Exponential stability of an invariant torus of a nonlinear countable system of differential equations
zbMATH Open document ID: 0705.34057
DOI: 10.1007/BF01057025
author: P. I. Avdeyuk
author: Y. V. Teplinsky
published in: Ukrainian Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: Consider the nonlinear denumerable system of differential equations (*): \(d\phi /dt=a(\phi,h)\), \(dh/dt=P(\phi,h)h+c(\phi),\) where \(\phi =(\phi_ 1,\phi_ 2,...,\phi_ m)\), \(h=(h_ 1,h_ 2,...)\), a(\(\phi\),h), c(\(\phi\)) are continuous vector functions, \(P(\phi,h)=(p_{ij}(\phi,h))^{\infty}_{i,j=1}\) is an infinite matrix function, and \(\phi\) is periodic in \(\phi_ i\) with \(2\pi\)-period. The author gives some conditions under which any trajectory starting from a small neighborhood of an invariant torus of system (*) exponentially approaches a certain trajectory on the torus.
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 4156977
zbMATH Keywords: nonlinear denumerable system of differential equations
MaRDI profile type: Publication
cites work: Q5630017
cites work: Q3739485
description: scientific article; zbMATH DE number 4156977