中文摘要：

本文对紧致度量空间上的连续半流引入了几类原像熵的定义，并对它们的性质进行了研究．证明了对于无不动点的连续半流而言，这些熵具有一定程度的拓扑共轭不变性，对这些熵的关系进行了研究并得到了联系这些熵的不等式，还证明了连续半流与其时刻1映射具有相同的拓扑熵和原像熵。

英文摘要：

In this paper, several preimage entropies for semi-flows on compact metric spaces are introduced and studied. We prove that most of these entropies are invariant in a certain sense under conjugacy when the semi-flows under consideration are free of fixed points. The relation between these entropies is studied and an inequality relating them is given. It is also shown that most of these entropies for semi-flow are consistent with that for the time-1 mapping.