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Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

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arxiv 1906.09862 v6 pith:27URHHPH submitted 2019-06-24 math.DS

Peng Sun This is my paper · ORCID
classification math.DS
keywords intermediatemeasuresapproximatedynamicalentropiesergodicproductproperty
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For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and intermediate pressures are generic in certain subspaces. This proves a conjecture of Katok for a broad class of systems and extends a sequence of known results.

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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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