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Structure of bounded topological‐sequence‐entropy minimal systems
Author(s) -
Maass Alejandro,
Shao Song
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm080
Subject(s) - equicontinuity , topological entropy , mathematics , bounded function , sequence (biology) , tuple , extension (predicate logic) , topological entropy in physics , discrete mathematics , entropy (arrow of time) , combinatorics , dynamical systems theory , pure mathematics , topology (electrical circuits) , topological quantum number , computer science , physics , mathematical analysis , genetics , quantum mechanics , biology , programming language
In this article we prove that a minimal topological dynamical system ( X, T ) with bounded topological sequence entropy has the following structure.X⟵σ ′X ′↓ π↓ π ′X e q⟵τ ′Y ′Here π is the maximal equicontinuous factor of ( X, T ), σ ′ and τ ′ are proximal extensions and π ′ 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.