论文标题
子集拓扑压力的变分原理
Variational principles for topological pressures on subsets
论文作者
论文摘要
在本文中，我们研究了各种类型的拓扑压力与不同版本的测量压力之间的关系。我们扩展了风水的变化原理，用于包装压力，并分别为Pesin-Pitskel和堆积压力获得两个新的变化原理。我们表明，相对于潜在函数的各种类型的katok压力等于该度量的量度理论熵和潜在函数的组成部分。此外，我们获得了Billingsley Type定理的包装压力，这表明可以通过度量理论的局部压力来确定填料压力，以及对任何不变的Ergodic Borel概率度量的一组通用点的填料压力的变异原理。
In this paper, we investigate the relations between various types of topological pressures and different versions of measure-theoretical pressures. We extend Feng- Huang's variational principle for packing entropy to packing pressure and obtain two new variational principles for Pesin-Pitskel and packing pressures respectively. We show that various types of Katok pressures for an ergodic measure with respect to a potential function are equal to the sum of measure-theoretic entropy of this measure and the integral of the potential function. Moreover, we obtain Billingsley type theorem for packing pressure, which indicates that packing pressure can be determined by measure-theoretic upper local pressure of measures, and a variational principle for packing pressure of the set of generic points for any invariant ergodic Borel probability measure.
