Diophantine approximation of the orbits in topological dynamical systems
type: Item
instance of: scholarly article
title: Diophantine approximation of the orbits in topological dynamical systems
zbMATH Open document ID: 1442.37031
author: Chao Ma
author: Jun Wu
author: Baowei Wang
published in: Discrete and Continuous Dynamical Systems
publication date: 2019-03-28T00:00:00Z
review text: The present article deals with topological dynamical systems. The main attention is given to the set of points whose orbit can well approximate a given point infinitely often. A formulation of the main problem is ``a general principle for the shrinking target problem in a topological dynamical system''. The authors note that one of the main goals of this paper is to find a general principle for the topological entropy about the topological version of the shrinking target problem in systems as general as possible. It is shown that if a system \((X; T)\) satisfies the specification property, then the entropy transference principle holds true. Here \((X; T)\) is a compact metric space and \(T : X \to X\) is a continuous transformation on \(X\).
reviewed by: Symon Serbenyuk
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37B05
Mathematics Subject Classification ID: 37B02
zbMATH DE Number: 7044106
zbMATH Keywords: shrinking target
zbMATH Keywords: topological entropy
zbMATH Keywords: specification
MaRDI profile type: Publication
full work available at URL: dcds.2019104
OpenAlex ID: W2910506549
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Wikidata QID: Q128522545
DOI: 10.3934/DCDS.2019104
description: scientific article; zbMATH DE number 7044106