Entropy of a skew product with a \(Z^ 2\)-action
type: Item
instance of: scholarly article
title: Entropy of a skew product with a \(Z^ 2\)-action
zbMATH Open document ID: 0868.28011
published in: Pacific Journal of Mathematics
publication date: 1996-08-29T00:00:00Z
review text: This paper deals with the entropy of a skew product with a \(Z^2\) action generated by a cellular automaton (i.e., one of the generators of the \(Z^2\) action is generated by a block map). The cone entropy and the directional entropy are first proved to be the same for such a \(Z^2\) action. Then the author considers the entropy of a dynamical system generated by a skew product, where there is a \(Z^2\) action defined by a cellular automaton on the second fiber. In this case, the fiber contribution to the entropy is proved to be equal to the directional entropy in the direction of the integral of the skewing function, as expected from the classical case where \(Z\) acts on the two fibers.
Mathematics Subject Classification ID: 28D20
Mathematics Subject Classification ID: 68Q80
Mathematics Subject Classification ID: 28D15
zbMATH DE Number: 910255
zbMATH Keywords: skew product
zbMATH Keywords: \(Z^ 2\) action
zbMATH Keywords: cellular automaton
zbMATH Keywords: block map
zbMATH Keywords: cone entropy
zbMATH Keywords: directional entropy
author: Kyewon K. Park
reviewed by: Valérie Berthé
MaRDI profile type: Publication
full work available at URL: pjm.1996.172.227
OpenAlex ID: W1531491048
DOI: 10.2140/PJM.1996.172.227
description: scientific article; zbMATH DE number 910255