We show that for every topological dynamical system with approximate product property, zero topological entropy is equivalent to unique ergodicity. This indicates that for such a system, the structure of the space of invariant measures is determined by its topological entropy.
Ergodic measures of intermediate entropies for dynamical systems with approximate product property
The Structure on Invariant Measures of $C^1$ generic diffeomorphisms
Properties of invariant measures in dynamical systems with the shadowing property
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