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Entropies of automorphisms of a topological Markov shift

Author: D. A. Lind
Journal: Proc. Amer. Math. Soc. 99 (1987), 589-595
MSC: Primary 54H20; Secondary 28D20, 54C70, 58F11
MathSciNet review: 875406
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Abstract: Let $ \sigma $ be a mixing topological Markov shift, $ \lambda $ a weak Perron number, $ q\left( t \right)$ a polynomial with nonnegative integer coefficients, and $ r$ a non-negative rational. We construct a homeomorphism commuting with $ \sigma $ whose topological entropy is $ \log {\left[ {q\left( \lambda \right)q\left( {1/\lambda } \right)} \right]^r}$. These values are shown to include the logarithms of all weak Perron numbers, and are dense in the nonnegative reals.

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Keywords: Topological entropy, Perron number, automorphism group of a topological Markov shift
Article copyright: © Copyright 1987 American Mathematical Society

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