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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Some examples of sequence entropy as an isomorphism invariant


Author: F. M. Dekking
Journal: Trans. Amer. Math. Soc. 259 (1980), 167-183
MSC: Primary 28D20
DOI: https://doi.org/10.1090/S0002-9947-1980-0561831-2
MathSciNet review: 561831
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Abstract: With certain geometrically diverging sequences A and the shift T on dynamical systems arising from substitutions we associate a Markov shift S such that the A-entropy of T equals the usual entropy of S. We present examples to demonstrate the following results. Sequence entropy can distinguish between an invertible ergodic transformation and its inverse. A-entropy does not depend monotonically on A. The variational principle for topological sequence entropy need not hold.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0561831-2
Keywords: Sequence entropy, topological sequence entropy, substitution, Markov shift
Article copyright: © Copyright 1980 American Mathematical Society