Lipschitz invariant tori of indefinite-monotone systems
type: Item
instance of: scholarly article
title: Lipschitz invariant tori of indefinite-monotone systems
zbMATH Open document ID: 1267.37063
author: I. O. Parasyuk
author: V. A. Lahoda
author: A. M. Samojlenko
published in: Ukrainian Mathematical Journal
publication date: 2013-01-03T00:00:00Z
review text: The authors study dynamical systems \(\dot{\varphi}=a(\varphi,x)\), \(\dot{x}=b(\varphi,x)\), where \(\varphi\) is a point in the \(m\)-dimensional torus \( \mathbb{T}^m\) and \(x \) in the \(n\)-dimensional Euclidean space \( \mathbb{R}^n\). Under some sufficient conditions (like indefinite coercivity and indefinite monotonicity) for the functions \(a\) and \(b\), an existence theorem for invariant tori \(x=u(\varphi)\) is proved. This proof is based on the topological Wazewski principle, the Schauder fixed-point theorem and the so-called \(V\)-\(W\)-pair of a guiding function \(W\) and estimating function \(V\). No example is given.
Mathematics Subject Classification ID: 37J40
zbMATH DE Number: 6121526
zbMATH Keywords: invariant tori
reviewed by: Angel Zhivkov
MaRDI profile type: Publication
full work available at URL: s11253-012-0655-8
OpenAlex ID: W2046392945
cites work: Q5630017
cites work: Perturbation theory of smooth invariant tori of dynamical systems
cites work: Q5622592
cites work: Q5658861
cites work: Q4233735
cites work: Existence of an invariant torus for a class of systems of differential equations
cites work: Q3553044
cites work: Some modern aspects of the theory of impulsive differential equations
cites work: On the existence of an invariant torus for an essentially nonlinear system of differential equations
cites work: Stable and conditionally stable almost-periodic solutions of V-monotone systems
cites work: Q4422352
cites work: Q3682800
cites work: Existence of \(V\)-bounded solutions for non-autonomous nonlinear systems via the Ważewski topological principle
DOI: 10.1007/S11253-012-0655-8
description: scientific article; zbMATH DE number 6121526