标题： 可换群作用下子集的BS维数的变分原理 显示英文标题

标题： Variational principles for BS dimension of subsets under amenable group actions

摘要： 在本文中，我们关注在可解群作用下BS维数和BS填充维数的研究。 首先，我们得到两个Bowen方程，这些方程说明了在可解群作用下BS维数与Pesin-Pitskel拓扑压力之间的关系，以及BS填充维数与在可解群作用下填充拓扑压力之间的关系。 此外，我们在可解群作用下建立了BS维数和BS填充维数的变分原理和逆变分原理。 显示英文摘要

摘要： In this manuscript, we focus on the investigation of the BS dimension and BS packing dimension under amenable group actions. Firstly, we obtain two Bowen's equations which illustrate the relation of BS dimension to the Pesin-Pitskel topological pressure under amenable group actions, and BS packing dimension to the packing topological pressure under amenable group actions. Moreover, we establish the variational principle and inverse variational principle for BS dimension and BS packing dimension under amenable group actions.