Point-to-periodic and periodic-to-periodic connections
type: Item
instance of: scholarly article
title: Point-to-periodic and periodic-to-periodic connections
zbMATH Open document ID: 1052.65113
author: Luca Dieci
author: Jorge Rebaza
published in: BIT
publication date: 2004-08-06T00:00:00Z
review text: The authors consider computing and continuing connecting orbits in parameter dependent dynamical systems. Some details of algorithms for computing connections between equilibria and periodic orbits, and between periodic orbits are given. The theoretical foundation of these techniques is given in the seminal work of \textit{W.-J. Beyn} [Contemp. Math. 172, 131--168 (1994; Zbl 0813.58046)], where a numerical technique is proposed. The algorithms consist of splitting the computation of the connection from that of the periodic orbit(s). To set up appropriate boundary conditions, the authors follow the algorithmic approach used by \textit{J. W. Demmel, L. Dieci} and {M. J. Friedman} [SIAM J. Sci. Comput. 22, No. 1, 81--94 (2000; Zbl 0967.34008)], for the case of connecting orbits between equilibira, and construct and exploit the smooth block Schur decomposition of the monodromy matrices associated to the periodic orbits. Numerical examples illustrate the performance of the algorithms. Finally, it should be mentioned that the paper contains many misprints that invalid some technical results so that a complete revision would be desirable.
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 37C27
zbMATH DE Number: 2081528
zbMATH Keywords: connecting orbits
zbMATH Keywords: periodic orbits
zbMATH Keywords: projection boundary conditions
zbMATH Keywords: continuation of invariant subspaces
zbMATH Keywords: monodromy matrix
zbMATH Keywords: algorithms
zbMATH Keywords: Schur decomposition
zbMATH Keywords: numerical examples
reviewed by: Manuel Calvo
MaRDI profile type: Publication
DOI: 10.1023/B:BITN.0000025093.38710.F6
description: scientific article; zbMATH DE number 2081528