Sequence entropy pairs and complexity pairs for a measure

Wen Huang[1]; Alejandro Maass; Xiangdong Ye

  • [1] University of Science and Technology of China, Department of Mathematics, Hefei, Anhui, 230026 P.R. (Chine), Universidad de Chile, Departamento de Ingeniería 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 (2004)

  • Volume: 54, Issue: 4, page 1005-1028
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Huang, Wen, Maass, Alejandro, and Ye, Xiangdong. "Sequence entropy pairs and complexity pairs for a measure." Annales de l’institut Fourier 54.4 (2004): 1005-1028. <http://eudml.org/doc/116128>.

@article{Huang2004,
abstract = {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.},
affiliation = {University of Science and Technology of China, Department of Mathematics, Hefei, Anhui, 230026 P.R. (Chine), Universidad de Chile, Departamento de Ingeniería 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)},
author = {Huang, Wen, Maass, Alejandro, Ye, Xiangdong},
journal = {Annales de l’institut Fourier},
keywords = {sequential entropy; complexity},
language = {eng},
number = {4},
pages = {1005-1028},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sequence entropy pairs and complexity pairs for a measure},
url = {http://eudml.org/doc/116128},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Huang, Wen
AU - Maass, Alejandro
AU - Ye, Xiangdong
TI - Sequence entropy pairs and complexity pairs for a measure
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 4
SP - 1005
EP - 1028
AB - 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.
LA - eng
KW - sequential entropy; complexity
UR - http://eudml.org/doc/116128
ER -

References

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