标题： 可接受群作用下的BS维数的变分原理 显示英文标题

标题： Variational principles for BS dimension 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，我们得到一个Bowen方程，该方程说明了在可解群作用下BS填充维数与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。 最后，我们还得到了在可解群作用下BS填充维数的Billingsley类型定理的类似结果。 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 a Bowen's equation which illustrate the relation of 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. Finally, we also get an analogue of Billingsley's type theorem for BS packing dimension under amenable group actions.