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Journal of the London Mathematical Society Advance Access originally published online on November 15, 2007
Journal of the London Mathematical Society 2007 76(3):702-718; doi:10.1112/jlms/jdm080
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© 2007 London Mathematical Society

Structure of bounded topological-sequence-entropy minimal systems

Alejandro Maass

Centro de Modelamiento Matemático and Departamento de Ingeniería Matemática
Universidad de Chile
Avenue Blanco Encalada 2120
Santiago, Chile

Song Shao

Department of Mathematics
University of Science and Technology of China
Hefei
Anhui 230026
PR China
songshao{at}ustc.edu.cn

In this article we prove that a minimal topological dynamical system (X, T) with bounded topological sequence entropy has the following structure.


Formula

Here {pi} is the maximal equicontinuous factor of (X, T), {sigma}' and {tau}' are proximal extensions and {pi}' is a finite-to-one equicontinuous extension. In order to prove this result we consider sequence entropy tuples and give their complete relation with regionally proximal tuples.

2000 Mathematics Subject Classification 37B40, 37B05 (primary).

Received November 28, 2006; published online November 15, 2007.


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