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Graphs with pre-assigned Salama entropies and optimal degrees for locally compact Markov shifts

Published online by Cambridge University Press:  01 August 2003

DORIS FIEBIG
DORIS FIEBIG
Affiliation:
Institut für Mathematische Stochastik, Universität Göttingen, Lotzestr. 13, 37083 Göttingen, Germany (e-mail: fiebig@math.uni-goettingen.de)
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Abstract

Suppose that S is a transitive locally compact Markov shift with Gurevic entropy less than log p, where p is an integer. If the inequality is strict, then S admits a graph presentation with degree p. Additionally, we realize any pre-assigned values for the Salama entropies. This result is best possible, since there are examples of Gurevic entropy log p which do not admit a graph presentation with degree p. We also show that every non-compact locally compact Markov shift has presentations without synchronizing blocks.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 4 , August 2003 , pp. 1093 - 1124
Copyright
2003 Cambridge University Press

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Footnotes

The paper is a revised version of a part of the authors Habilitationsschrift (Universität Heidelberg, 1998).