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Entropies of automorphisms of a topological Markov shift. (English) Zbl 0619.54030
Let \(\sigma\) be a mixing topological Markov shift, \(\lambda\) a weak Perron number, q(t) a polynomial with nonnegative integer coefficients, and r a nonnegative rational. We construct a homeomorphism commuting with \(\sigma\) whose topological entropy is \(\log [q(\lambda)q(1/\lambda)]^ r\). These values are shown to include the logarithms of all weak Perron numbers, and are dense in the nonnegative reals.

MSC:
54H20 Topological dynamics (MSC2010)
54C70 Entropy in general topology
37A99 Ergodic theory
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