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.
Ergodic measures of intermediate entropies for dynamical systems with the approximate product property
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abstract
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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Unique ergodicity for zero-entropy dynamical systems with the approximate product property
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.