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.
J., Varandas, P.: Topological feat ures of flows with the reparametrized gluing orbit property
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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.