Sequence entropy pairs and complexity pairs for a measure

Huang, Wen; Maass, Alejandro; Ye, Xiangdong

doi:10.5802/aif.2041

Sequence entropy pairs and complexity pairs for a measure
[Paires d'entropie séquentielle et paires de complexité pour une mesure]

Huang, Wen ¹ ; Maass, Alejandro ; Ye, Xiangdong

¹ University of Science and Technology of China, Department of Mathematics, Hefei, Anhui, 230026 P.R. (Chine), Universidad de Chile, Departamento de Ingenier\'ia Matemática and Centro de Modelamiento Matemático, Casilla 170/3 correo 3, Santiago (Chili), University of Science and Technology of China, Department of Mathematics, Hefei, Anhui, 230026 P.R. (Chine)

Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1005-1028.

Résumé
Abstract

Dans cet article, nous étudions des facteurs topologiques entre le facteur de Kronecker et le facteur équicontinu maximal d’un système dynamique. Nous introduisons la notion de $n$ -tuple d’entropie séquentielle pour une mesure et nous prouvons que l’ensemble $n$ - tuple d’entropie sequentielle pour une mesure est contenu dans l’ensemble de $n$ -tuple d’entropie séquentielle topologique [H-Y]. La réciproque est fausse. Aussi en suivant les idées dans [BHM], nous introduisons une notion faible et une notion forte de paire de complexité pour une mesure. Nous prouvons que la notion forte est strictement contenue entre la notion de paire d’entropie et de paire de complexité topologique.

In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy $n$ -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity pair for a measure. We prove that in general the strongest notion is strictly contained in between sequence entropy pairs and topological complexity pairs.

MR Zbl

DOI : 10.5802/aif.2041

Classification : 54H20
Keywords: sequential entropy, complexity
Mot clés : entropie séquentielle, complexité

Affiliations des auteurs :

Huang, Wen ¹ ; Maass, Alejandro ; Ye, Xiangdong

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     title = {Sequence entropy pairs and complexity pairs for a measure},
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Huang, Wen; Maass, Alejandro; Ye, Xiangdong. Sequence entropy pairs and complexity pairs for a measure. Annales de l'Institut Fourier, Tome 54 (2004) no. 4, pp. 1005-1028. doi : 10.5802/aif.2041. http://www.numdam.org/articles/10.5802/aif.2041/

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