On constructing Markov partitions by computer
type: Item
instance of: scholarly article
title: On constructing Markov partitions by computer
zbMATH Open document ID: 0624.58036
DOI: 10.1007/BF01010527
author: Valter Franceschini
author: Fernando Zironi
published in: Journal of Statistical Physics
publication date: 1985-01-01T00:00:00Z
review text: Two methods to construct Markov partitions for two-dimensional systems are proposed. One is based on the existence of a known, or easily accessible by numerical analysis, hyperbolic fixed points; the other one, which is more general, is derived from Bowen's proof of the existence theorem of Markov partitions for hyperbolic systems. The methods are successfully implemented in two cases of hyperbolic systems: the linear automorphism \(\left( \begin{matrix} 1\\ 1\end{matrix} \begin{matrix} 1\\ 2\end{matrix} \right)\) of the 2-torus and a nonlinear perturbation of it. The methods are applied also to the Hénon mapping. In such nonhyperbolic case, however, they produce partitions of the Hénon attractor which lack some essential properties.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 37D99
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4013599
zbMATH Keywords: symbolic dynamics
zbMATH Keywords: stable and unstable manifolds
zbMATH Keywords: hyperbolic fixed points
zbMATH Keywords: Markov partitions
zbMATH Keywords: hyperbolic systems
zbMATH Keywords: Hénon attractor
MaRDI profile type: Publication
cites work: Q3963279
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description: scientific article; zbMATH DE number 4013599