真映射生成半群的拓扑压

张文杰; 杨荣领

doi:10.12052/gdutxb.190126

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真映射生成半群的拓扑压

更新时间：2026-05-27

- 真映射生成半群的拓扑压
- The Topological Pressure of a Semigroup Action Generated by Proper Maps
- 广东工业大学学报 2020年37卷第3期页码：59-62
- 作者机构：
  
  1. 华南理工大学数学学院,广东,广州,510641
  2. 华南理工大学广州学院,广东,广州,510800
- 作者简介：
  
  张文杰(1993–)，女，硕士研究生，主要研究方向为拓扑动力系统与遍历理论
- 基金信息：
  
  国家自然科学基金资助项目(11671149);广东省自然科学基金资助项目(2014A030313230);中央高校基础研究基金资助项目(SCUT(2015ZZ055;2015ZZ127))
- DOI：10.12052/gdutxb.190126
  中图分类号： O189.1
- 网络首发：2020-05-12，
  
  纸质出版：2020
- 稿件说明：
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张文杰, 杨荣领. 真映射生成半群的拓扑压[J]. 广东工业大学学报, 2020, 37(3): 59-62.

Zhang Wen-jie, Yang Rong-ling. The Topological Pressure of a Semigroup Action Generated by Proper Maps[J]. 2020, 37(3): 59-62.
张文杰, 杨荣领. 真映射生成半群的拓扑压[J]. 广东工业大学学报, 2020, 37(3): 59-62. DOI： 10.12052/gdutxb.190126.

Zhang Wen-jie, Yang Rong-ling. The Topological Pressure of a Semigroup Action Generated by Proper Maps[J]. 2020, 37(3): 59-62. DOI： 10.12052/gdutxb.190126.

摘要

在Biś和Patrão定义的拓扑熵基础上给出了度量空间中有限个真映射构成的半群的拓扑压

并证明了局部紧可分度量空间上由真映射构成的自由半群的拓扑压和它的一点紧化空间上对应的拓扑压相等

在此基础上给出真映射构成的半群的拓扑压的性质。

Abstract

As an extension of topological entropy

topological pressure was first proposed by Ruelle in 1973

and then further extended by Walters to compact metric spaces of continuous maps. It reflects the complexity of dynamic system

and it is an important research content in fractal geometry and dynamic system. In order to solve more complex problems relevant to topological pressure

more and more new research has emerged. On the basis of the topological entropies defined by Biś and Patrão

the topological pressure of a semigroup action generated by proper maps of the metric space is given

and then the topological pressure of a free semigroup action generated by proper maps in a locally compact separable metric space is proved

which is equivalent to the topological pressure of a free semigroup action in its one-point compactification space. Furthermore

some properties of the topological pressure of a free semigroup action are given.

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references

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WALTERS P. An introduction to ergodic theory [M]. New York: Springer-Verlag, Heidelberg, Berlin, 1982.

PESIN Y B , PITSKEL B S. Topological pressure and the variational principle for noncompact sets [J]. Functional Analysis and Its Applications, 1984, 18(4): 307-318.

BARREIRA, LUIS M. A non-additive thermodynamic formalism and applications to dimension theory of hyperbolic dynamical systems [J]. Ergodic Theory and Dynamical Systems, 1996, 16(5): 871-927.

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BUFETOV A. Topological entropy of free semigroup actions and skew-product transformations [J]. Journal of Dynamical and Control Systems, 1999, 5(1): 137-143.

MA D K, LIU S H. Some properties of topological pressure of a semigroup of continuous maps [J]. Dynamical System, 2014, 29(1): 1-17.

LIN X G, MA D K, WANG Y P. On the measure-theoretic entropy and topological pressure of free semigroup actions [J]. Ergodic Theory and Dynamical Systems, 2016, 38(2): 1-37.

PATRÃO, MAURO. Entropy and its variational principle for non-compact metric spaces [J]. Ergodic Theory and Dynamical Systems, 2010, 30(5): 1529-1542.

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