可数Amenable群作用的可测势函数的拓扑压

Topological Pressure for Measurable Potentials of Amenable Group Actions

【目的】在Amenable群作用下,给出相应的质量分布原理。【方法】综合运用了拓扑学、遍历论与几何测度论的方法。【结果】对任何可测势函数,引入了拓扑压、测度意义压的定义,并证明了相应了质量分布原理。【结论】对于可测势函数,存在相应的质量分布原理。

[Purposes]To give the corresponding mass distribution principle under the action of amenable group.[Methods]The methods of topology,ergodic theory and geometric measure theory were used comprehensively.[Findings]For any measurable potential function,the definitions of topological pressure and measure meaning pressure are introduced,and the corresponding mass distribution principle is proved.[Conclusions]For the measurable potential function,there is a corresponding mass distribution principle.