Relativization of dynamical properties
type: Item
instance of: scholarly article
title: Relativization of dynamical properties
zbMATH Open document ID: 1262.37004
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: The author presents recent developments in the relative topological dynamics. Mainly, he reviews some recent results on the relative Li-York chaos, relative topological entropy, relative variational principle, relative entropy pair, relative topological Pinsker factor, relative positive entropy and relative uniform positive entropy. Let us recall that for any topological dynamical system \((X,T)\), where \(X\) is a metric compact space and \(T\) a homeomorphism on \(X\), the dynamical system \((Y,S)\) is said to be a factor of \(X\) if there is a continuous surjective map \(\pi\) from \(X\) to \(Y\) such that \(\pi \circ T= S \circ \pi\). The dynamical property holds relatively if it holds relatively with respect to the factor map \(\pi\).
Mathematics Subject Classification ID: 37A05
Mathematics Subject Classification ID: 37A35
zbMATH DE Number: 6131969
zbMATH Keywords: relative entropy
zbMATH Keywords: asymptotic pair
zbMATH Keywords: scrambled set
zbMATH Keywords: local variational principales
zbMATH Keywords: relative Pinsker factor
zbMATH Keywords: relative complete positive entropy
zbMATH Keywords: relative uniform entropy
author: Guohua Zhang
reviewed by: El Houcein El Abdalaoui
MaRDI profile type: Publication
full work available at URL: s11425-011-4332-4
OpenAlex ID: W1966107942
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Relativization of dynamical properties (DOI)
DOI: 10.1007/S11425-011-4332-4