正则脉冲半流的拓扑熵和度量熵
Topological entropy and metric entropy for regular impulsive semiflows
摘要：
在arXiv：1801.01238中，引入了Bowen的拓扑熵的一个变体，它可以应用于紧致度量空间上的不连续半流的研究。主要的新颖之处是使用某些家庭的pseudosemetrics相关联的半流，在这样一种方式，在连续的情况下，他们符合经典的鲍文熵。证明了正则脉冲半流可以通过一致连续双射与定义在紧度量空间中的某个连续半流进行共轭。在所引用的论文中，熵由分离集的增长率定义。本文的主要结果表明，对于正则脉冲半流，用生成集定义的熵与用分离集定义的熵是一致的。此外，熵的概念满足一个变分原理。这一结果是通过对相关的伪半度量族作一点改变而得到的。
英文摘要：
In arXiv:1801.01238 a variation of Bowen's topological entropy that can be applied to the study of discontinuous semiflows on compact metric spaces was introduced. The main novetly is the use of certain family of pseudosemimetrics associated to the semiflow, in a such a way that in the continuous case they coincide with the classical Bowen's entropies. It was proved that regular impulsive semiflow can be semiconjugated by uniformly continuous bijection to certain continuous semiflow defined in a compact metric space. In the cited paper, the entropy is defined by the growth rate of separated sets. The main results of the present work is show that, for regular impulsive semiflows, the entropy defined by using spanning sets agrees with the entropy using separated sets. Moreover, this notion of entropy satisfy a variational principle. This results are obtained introducing a little change on the family of pseudosemimetrics associated to.
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