Multiplicity of fixed points and growth of \(\varepsilon \)-neighborhoods of orbits
type: Item
instance of: scholarly article
title: Multiplicity of fixed points and growth of \(\varepsilon \)-neighborhoods of orbits
zbMATH Open document ID: 1263.37069
author: Pavao Mardešić
author: Maja Resman
author: Vesna Županović
published in: Journal of Differential Equations
publication date: 2012-09-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1108.4707
review text: The multiplicity of a fixed point is studied for nondifferentiable functions along the lines initiated by the third author jointly with \textit{N. Elezović} and \textit{D. Žubrinić} [Chaos Solitons Fractals 34, No. 2, 244--252 (2007; Zbl 1133.37007)] in a differentiable case. The estimation of the multiplicity is this time obtained in a more sophisticated way. More precisely, an appropriate scale is found to which the length of the \(\varepsilon\)-neighbourhood of the close orbits is comparable. Several applications are presented, including those to particular Poincaré maps.
reviewed by: Jan Andres
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6081510
zbMATH Keywords: multiplicity
zbMATH Keywords: fixed points
zbMATH Keywords: nondifferentiable functions
zbMATH Keywords: limit cycles
MaRDI profile type: Publication
OpenAlex ID: W1575078891
arXiv ID: 1108.4707
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DOI: 10.1016/J.JDE.2012.06.020
description: scientific article; zbMATH DE number 6081510