Topological dynamics: rigorous numerics via cubical homology
type: Item
instance of: scholarly article
zbMATH Open document ID: 1269.37019
author: Marian Mrozek
publication date: 2012-09-14T00:00:00Z
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 37B30
Mathematics Subject Classification ID: 37M99
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 55-04
Mathematics Subject Classification ID: 55N35
zbMATH DE Number: 6082691
zbMATH Keywords: computer assisted proof
zbMATH Keywords: rigorous numerics
zbMATH Keywords: interval arithmetic
zbMATH Keywords: chaotic dynamics
zbMATH Keywords: Conley index
zbMATH Keywords: index pair
zbMATH Keywords: cubical set
zbMATH Keywords: homology algorithm
zbMATH Keywords: reduction methods
MaRDI profile type: Publication
title: Topological dynamics: rigorous numerics via cubical homology
review text: The paper presents an overview of a method of computer assisted proofs in dynamics, developed mainly by the author and his collaborators. The method is based on the Conley index theory and makes use of computations of homology of some cubical sets and maps, frequently obtained by a numerical approximation of systems of ordinary differential equations. Examples of applications include proofs of the existence of complicated dynamics in the Lorenz equations and the Hénon map, time series analysis of experiments, and databases for multiparameter systems.NEWLINENEWLINEFor the entire collection see [Zbl 1245.55001].
reviewed by: Roman Srzednicki
description: scientific article; zbMATH DE number 6082691