非紧集上错误函数下自由半群作用的拓扑压  

Topological pressure of free semigroup actions under a mistake function for non-compact sets

作　　者：郭锴 肖倩 马东魁 GUO Kai;XIAO Qian;MA Dongkui(School of Mathematics,South China University of Technology,Guangzhou 510641,China)

机构地区：[1]华南理工大学数学学院,广东广州510641

出　　处：《中山大学学报（自然科学版）（中英文）》2022年第6期180-189,共10页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11771149)。

摘　　要：拓扑压是动力系统和遍历理论中的核心概念,它在热力学形式的研究中具有重要作用。随着物理过程的演化,演化过程在轨道计算中产生变化或误差是很自然的。然而,一个自适应系统应该随着时间的推移减少误差。本文利用C-P结构给出了错误函数下自由半群作用的拓扑压的两个定义并证明它们是等价的,此外,还证明了非紧集上错误函数下自由半群作用的拓扑压和没有错误函数下自由半群作用的拓扑压是等价的。最后,应用上述定理举例证明了平均度量下的自由半群作用的拓扑压等价于Bowen度量下的自由半群作用的拓扑压。Topological pressure is a core concept of dynamic systems and ergodic theory,which plays an important role in the study of thermodynamic formalism.As the physical process evolves,it is natural for the evolution process to produce changes or some errors in the orbit calculation.However,a self-adaptable system should decrease errors over time.In this paper,we introduce two definitions of topological pressure of free semigroup actions under a mistake function by using C-P structure and prove that they are equivalent.Furthermore,we show that the topological pressure of free semigroup actions under a mistake function on a non-compact subset is equivalent to the topological pressure of free semigroup actions of the subset without mistake function.As an application,we use the above theorem to show that the topological pressure of free semigroup actions defined by mean metric is equivalent to the topological pressure of free semigroup actions defined by Bowen metric.

关 键 词：自由半群作用 拓扑压 错误函数 平均度量 C-P结构 

分 类 号：O193[理学—数学]