Computational hyperbolicity
type: Item
instance of: scholarly article
title: Computational hyperbolicity
zbMATH Open document ID: 1214.37026
author: Marcin Mazur
author: Jacek Tabor
published in: Discrete and Continuous Dynamical Systems
publication date: 2011-03-15T00:00:00Z
review text: Nowadays, computers are quite often used for proving theorems whose direct analytic verification is not possible. The paper under review deals with the problem of computer assisted proof of hyperbolicity of a given set using a concept of semihyperbolicity. Taking into account that semihyperbolicity does not require the splitting of the space to be invariant, it can be directly and relatively easily verified through a direct numerical computation. For example, the authors prove hyperbolicity of the celebrated Hénon attractor associated with the Hénon map of the real plane into itself, \[ H_{a,b}:(x,y) \mapsto(a-x^{2}+by,x) , \] for \(a=5.4\) and \(b=-1\) in less than 10 seconds on a 2 GHz personal computer.
Mathematics Subject Classification ID: 37D05
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 5866081
zbMATH Keywords: dynamical systems
zbMATH Keywords: hyperbolicity
zbMATH Keywords: computer assisted proof
zbMATH Keywords: semihyperbolicity
zbMATH Keywords: Hénon attractor
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: dcds.2011.29.1175
OpenAlex ID: W4250404695
Wikidata QID: Q112226034
DOI: 10.3934/DCDS.2011.29.1175
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description: scientific article; zbMATH DE number 5866081