论文标题
抽象的熵和扩张
Abstract entropy and expansiveness
论文作者
论文摘要
我们在预订的半群中介绍了熵的一般定义，从而扩展了拓扑熵的概念。根据我们的定义，我们获得了文献中遇到的各种类似熵的理论所表现出的基本特性，其中许多是我们计划的特殊情况。我们展示了如何从混凝土案例中抽象熵对应性属性的特性得出。我们还在这种一般环境中引入了广泛性的概念，扩展了扩展动力学系统的概念，该概念与熵的方式与拓扑动态相似。最后，作为一种应用，我们建议在具体情况下对新熵和扩张性的一些定义。
We present a general definition of entropy in the setting of pre-ordered semigroups, extending the notion of topological entropy. From our definition, we obtain the basic properties exhibited by various entropy-like theories encountered in the literature, many of them being particular cases of our scheme. We show how to derive from the properties of the abstract entropy corresponding properties in the concrete cases. We also introduce a notion of expansiveness in this general context, extending the concept of expansive dynamical system, which is related to the entropy in a similar fashion as in the case of topological dynamics. Finally, as an application, we suggest some definitions of new entropies and expansiveness in concrete cases.
