We show that for every topological dynamical system with approximate product property, zero topological entropy is equivalent to unique ergodicity. Hence the space of invariant measures for such a system is a Poulsen simplex if and only if the topological entropy is positive. Equivalence of minimality is also discussed. Some examples are included.

中文翻译：

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具有近似乘积性质的零熵动力系统的唯一遍历性

我们表明，对于每个具有近似乘积性质的拓扑动力系统，零拓扑熵等价于唯一遍历性。因此，当且仅当拓扑熵为正时，此类系统的不变测度空间是 Poulsen 单纯形。还讨论了最小化的等效性。包括一些示例。