Numerical computation of rotation numbers of quasi-periodic planar curves
type: Item
instance of: scholarly article
title: Numerical computation of rotation numbers of quasi-periodic planar curves
zbMATH Open document ID: 1190.37048
author: Alejandro Luque
author: Jordi Villanueva
published in: Physica D
publication date: 2009-11-18T00:00:00Z
review text: The authors present numerical algorithms to deal with quasi-periodic invariant curves of planar maps by adapting a method given by \textit{T. M. Seara} and \textit{J. Villanueva} [Physica D 217, No.~2, 107--120 (2006; Zbl 1134.37339)] to compute rotation numbers of an analytic circle diffeomorphisms. The approach consists in computing a suitable average of the iterates of the map to obtain a new curve for which the direct projection onto a circle is well posed. This method can be applied to more general contexts because the construction does not use the invariance of the quasi-periodic curve under the map. Several examples are given to illustrate the method.
reviewed by: Zaihong Wang
Mathematics Subject Classification ID: 37E45
Mathematics Subject Classification ID: 37C05
Mathematics Subject Classification ID: 37M05
zbMATH DE Number: 5634863
zbMATH Keywords: invariant curves
zbMATH Keywords: rotation number
zbMATH Keywords: non-twist maps
zbMATH Keywords: numerical approximation
describes a project that uses: QD
MaRDI profile type: Publication
full work available at URL: j.physd.2009.07.014
OpenAlex ID: W2153573293
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DOI: 10.1016/J.PHYSD.2009.07.014
description: scientific article; zbMATH DE number 5634863