Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors
type: Item
instance of: scholarly article
title: Towards a kneading theory for Lozi mappings. II: Monotonicity of the topological entropy and Hausdorff dimension of attractors
zbMATH Open document ID: 0945.37004
author: Yutaka Ishii
published in: Communications in Mathematical Physics
publication date: 2000-06-29T00:00:00Z
review text: The article is a sequel to \textit{Y. Ishii} [Nonlinearity 10, No.3, 731-747 (1997; Zbl 0908.58015)]. The articles develop symbolic dynamics for Lozi mappings \((x,y) \mapsto (1 - a |x|+ by , x)\), a piecewise linear caricature of the Hénon map. The first article introduces symbolic dynamics and the notions of pruning front and pruning pair. This article discusses some applications of these notions. In particular, it is shown that for each \(b \neq 0\), the topological entropy is a nondecreasing function of \(a\) once \(a\) is larger then some \(a_\ast(b)\) (which is smaller then the infimum of the values of \(a\) for which a full horseshoe exists). Monotonicity properties of bifurcations as \(a\) varies are also discussed. These results have been extended, for small values of \(b\), in \textit{Y. Ishii} and \textit{D. Sands} [Commun. Math. Phys. 198, 397-406 (1998; Zbl 0923.58019)]. The article under review also contains estimates for the Hausdorff dimension of the Lozi attractor in terms of the parameters.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 1213908
MaRDI profile type: Publication
full work available at URL: s002200050245
OpenAlex ID: W2025381354
DOI: 10.1007/S002200050245
description: scientific article; zbMATH DE number 1213908