Stability of mappings with spectrum on a unit circle
type: Item
instance of: scholarly article
title: Stability of mappings with spectrum on a unit circle
zbMATH Open document ID: 0858.39004
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-05-19T00:00:00Z
review text: The author considers the mapping (1) \(x^*=Ax+\sum^\infty_{j=2} F^{(j)}(x)\), where \(x\in\mathbb{R}^m\), the matrix \(A\) has \(g\) pairs of non-resonant complex eigenvalues with absolute values of unity and \(F^{(j)}(x)\) are \(m\)-dimensional vector-valued forms of the \(j\)th degree. Sufficient conditions for asymptotic stability and instability of the fixed point \(x=0\) of (1) are obtained. In the main case they are necessary and sufficient conditions.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 861855
zbMATH Keywords: system of difference equations
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: asymptotic stability
zbMATH Keywords: instability
zbMATH Keywords: fixed point
author: Ya. M. Gol'tser
reviewed by: Victor I. Tkachenko
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1447
OpenAlex ID: W2032000121
DOI: 10.1006/JMAA.1995.1447
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description: scientific article; zbMATH DE number 861855