Boundary influence on the entropy of a Lozi-type map
type: Item
instance of: scholarly article
title: Boundary influence on the entropy of a Lozi-type map
zbMATH Open document ID: 1205.39003
author: Jonq Juang
author: Yu-Chuan Chang
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-09-01T00:00:00Z
review text: The paper deals with \(n\)th-degree Lozi-type map \[ T(x,y) = (y, F(y) - bx), \] where \(F(y)\) is a continuous piece-wise linear function. This map is induced from a spatial discretization of a reaction-diffusion system. The authors solve open problems from the work by \textit{V. S. Afraimovich} and \textit{S. B. Hsu} [Lectures on chaotic dynamical systems. AMS/IP Studies in Advanced Mathematics 28. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (2003; Zbl 1152.37300)] and prove that the equalities \[ h(T) = h_D(T)= h_N(T) = h_{l(1),l(2)}(T) \] are not true in general. Here \(h(T)\) and \(h_{l(1),l(2)}(T)\) are the so-called spatial entropies of the map \(T\) and the spatial entropies of \(T\) with respect to the lines \(l(1)\) and \(l(2),\) and \(h_D(T)\) and \(h_N(T)\) are the spatial entropies with respect to the Dirichlet and Neuman boundary conditions. Sufficient conditions under which the equalities hold are given.
reviewed by: Victor I. Tkachenko
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 37A35
zbMATH DE Number: 5777347
zbMATH Keywords: Lozi-type map
zbMATH Keywords: entropy
zbMATH Keywords: boundary influence
zbMATH Keywords: dynamics of intersection
zbMATH Keywords: Smale-Horseshoe
zbMATH Keywords: reaction-diffusion system
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.06.004
OpenAlex ID: W2045202964
cites work: Q4803986
cites work: Q4357413
cites work: Q3479238
cites work: Q3927930
cites work: Bowen-Ruelle Measures for Certain Piecewise Hyperbolic Maps
cites work: Ergodic properties of the Lozi mappings
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cites work: Q3993502
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DOI: 10.1016/J.JMAA.2010.06.004
description: scientific article; zbMATH DE number 5777347