Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds
type: Item
instance of: scholarly article
title: Topological approach to rigorous numerics of chaotic dynamical systems with strong expansion of error bounds
zbMATH Open document ID: 1192.65152
author: Marian Mrozek
author: Roman Srzednicki
published in: Foundations of Computational Mathematics
publication date: 2010-04-28T00:00:00Z
review text: The authors construct an algorithm for a differential equation of the form \[ z'=(1+e^{i\eta t}|z|^{2})\overline{z}, \] where \(z\) is a complex function of the real variable \(t\) and \(\eta\) is a real parameter. The algorithm describes the set of points of the solution \(\varphi(t)\) for an interval \(( t_{0},t_{1})\), but does not solve the differential equation by using methods of numerical analysis.
Mathematics Subject Classification ID: 65P20
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 37B55
Mathematics Subject Classification ID: 37C25
zbMATH DE Number: 5702491
zbMATH Keywords: Poincaré map
zbMATH Keywords: invariant set
zbMATH Keywords: chaotic dynamical systems
zbMATH Keywords: error bounds
zbMATH Keywords: algorithm
describes a project that uses: RODES
describes a project that uses: CAPD
reviewed by: Ivan Secrieru
MaRDI profile type: Publication
full work available at URL: s10208-009-9053-5
OpenAlex ID: W2117233628
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DOI: 10.1007/S10208-009-9053-5
description: scientific article; zbMATH DE number 5702491