A lower estimate of the entropy of an automorphism and maximum entropy conditions for an invariant measure of a suspension flow over a Markov shiftстатья
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Аннотация:One of the two results in this paper is a lower estimate for the Kolmogorov–Sinai entropy of
an automorphism T of a measurable space X, which corresponds to a T-invariant probability measure
μ on X, in terms of the entropies of the same automorphis T corresponding to a sequence of T-invariant probability measures μ_n converging to μ in a certain sense. The second result, which is obtained by using the first one, gives conditions on an invariant measure of a suspension flow over a Markov shift under which the entropy of the flow with respect to this measure is maximal, i.e., coincides with the topological entropy.