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Computing the topological entropy of shifts
Author(s) -
Spandl Christoph
Publication year - 2007
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710014
Subject(s) - topological entropy , mathematics , digraph , computability , equivalence relation , equivalence (formal languages) , topological entropy in physics , entropy (arrow of time) , discrete mathematics , combinatorics , topology (electrical circuits) , pure mathematics , physics , topological quantum number , quantum mechanics
Different characterizations of classes of shift dynamical systems via labeled digraphs, languages, and sets of forbidden words are investigated. The corresponding naming systems are analyzed according to reducibility and particularly with regard to the computability of the topological entropy relative to the presented naming systems. It turns out that all examined natural representations separate into two equivalence classes and that the topological entropy is not computable in general with respect to the defined natural representations. However, if a specific labeled digraph representation – namely primitive, right‐resolving labeled digraphs – of some class of shifts is considered, namely the shifts having the specification property, then the topological entropy gets computable. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)