论文标题
包装拓扑熵用于符合的小组动作
Packing topological entropy for amenable group actions
论文作者
论文摘要
包装拓扑熵是包装维度的动态类比，可以将其视为Bowen拓扑熵的对应物。在本文中，我们将对连续的$ g $ ACTION动力系统$（x，g）$进行系统地研究包装拓扑熵，其中$ x $是一个紧凑的公制空间，$ g $是一个可计数的离散良好的组。 我们首先证明了适合包装拓扑熵的各种原则：对于任何$ x $的Borel子集$ z $，$ Z $的包装拓扑熵等于所有Borel概率的上限额外的额外距离$ Z $ z $具有全部措施。然后，我们获得了有关正式包装熵的熵不等式。最后，我们表明，如果$μ$是ergodic或系统满足某种规范属性，则任何不变的孔毛概率度量$μ$的填料拓扑熵与公制熵相吻合。
Packing topological entropy is a dynamical analogy of the packing dimension, which can be viewed as a counterpart of Bowen topological entropy. In the present paper, we will give a systematically study to the packing topological entropy for a continuous $G$-action dynamical system $(X,G)$, where $X$ is a compact metric space and $G$ is a countable discrete amenable group. We first prove a variational principle for amenable packing topological entropy: for any Borel subset $Z$ of $X$, the packing topological entropy of $Z$ equals the supremum of upper local entropy over all Borel probability measures for which the subset $Z$ has full measure. And then we obtain an entropy inequality concerning amenable packing entropy. Finally we show that the packing topological entropy of the set of generic points for any invariant Borel probability measure $μ$ coincides with the metric entropy if either $μ$ is ergodic or the system satisfies a kind of specification property.
