随着现代动力系统与遍历理论的发展，人们常常把研究的视角放在更为一般的群作用之下。其中amenable群作用动力系统是人们关注的中心之一。在此框架下，以维数理论为出发点的熵和压的研究才刚刚起步，相应的热力学形式的理论也尚未完善。为此，我们将致力于可数离散amenable群作用动力系统的熵、压与热力学形式的研究，并应用于amenable群作用动力系统的维数理论以及重分形分析。本项目的研究将有助于人们深入理解动力系统的几何结构、维数复杂性以及动力学集合的测度分布，同时也将有助于人们以更广阔的视角来认识Z与Z^d作用下的动力学性态。

With the development of modern dynamical system and ergodic theory, researchers usually take their perspectives in the frameworks for actions by more general groups. Among them the class of amenable groups actions is one of the foci. Studies on entropy and pressure inspired by dimension theory have just started under this framework; the theory of the corresponding thermodynamic formalism has not been complete as well. In this project, we will devote to the research on entropy、pressure and thermodynamic formalism for dynamical systems acting by countable discrete amenable groups. The research will provide deeper comprehension on the geometric structure、dimensional complexity and distribution of measures of dynamical sets in dynamical systems and will also make people understand dynamic behaviors for Z or Z^d actions with wider view point.