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Equilibrium states of intermediate entropies

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arxiv 2006.06358 v1 pith:EFC2TMFM submitted 2020-06-11 math.DS

classification math.DS
keywords conjectureentropiesequilibriumintermediatekatokstatesapplicationapproach
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We explore an approach to the conjecture of Katok on intermediate entropies that based on uniqueness of equilibrium states, provided the entropy function is upper semi-continuous. As an application, we prove Katok's conjecture for Ma\~n\'e diffeomorphisms.

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  1. Unique ergodicity for zero-entropy dynamical systems with the approximate product property

    math.DS 2019-08 conditional novelty 6.0 of 10

    Zero topological entropy is equivalent to unique ergodicity for every dynamical system with the approximate product property, with a minimality version under a stronger condition.

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