Relative entropy dimension of topological dynamical systems

Xiaomin Zhou

doi:10.3934/dcds.2019288

Article Contents

2019, Volume 39, Issue 11: 6631-6642. Doi: 10.3934/dcds.2019288

This issue Previous Article On the existence of full dimensional KAM torus for nonlinear Schrödinger equation Next Article Scattering of radial data in the focusing NLS and generalized Hartree equations

Relative entropy dimension of topological dynamical systems

Xiaomin Zhou

Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Received: January 31, 2019

Revised: March 31, 2019

Published: August 2019

(*) This research is supported by NSFC(11801193)

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Abstract

We introduce the notion of relative topological entropy dimension to classify the different intermediate levels of relative complexity for factor maps. By considering the dimension or ''density" of special class of sequences along which the entropy is encountered, we provide equivalent definitions of relative entropy dimension. As applications, we investigate the corresponding localization theory and obtain a disjointness theorem involving relative entropy dimension.

Keywords:

Relative entropy dimension,
relative dimension set.

Mathematics Subject Classification: Primary: 37B99, 54H20.

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