广东工业大学学报 ›› 2020, Vol. 37 ›› Issue (03): 59-62.doi: 10.12052/gdutxb.190126

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真映射生成半群的拓扑压

张文杰1, 杨荣领2   

  1. 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
  • 收稿日期:2019-10-10 出版日期:2020-05-12 发布日期:2020-05-12
  • 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
  • 基金资助:
    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））

The Topological Pressure of a Semigroup Action Generated by Proper Maps

Zhang Wen-jie1, Yang Rong-ling2   

  1. 1. School of Mathematics, South China University of Technology, Guangzhou 510641, China;
    2. Guangzhou College, South China University of Technology, Guangzhou 510800, China
  • Received:2019-10-10 Online:2020-05-12 Published:2020-05-12

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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。

关键词: 拓扑压, 自由半群, 真映射, 度量空间

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.

Key words: topological pressure, semigroup action, proper map, metric space

中图分类号: 

  • O189.1
[1] RUELLE D. Statistical mechanics on a compact set with ZpAction satisfying expansiveness and specification [J]. Transactions of the American Mathematical Society, 1973, 185: 237-251
[2] WALTERS P. An introduction to ergodic theory [M]. New York: Springer-Verlag, Heidelberg, Berlin, 1982.
[3] 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
[4] 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
[5] 胡超杰, 马东魁. 一些紧致系统的拓扑序列熵和广义specification性质[J]. 广东工业大学学报, 2007, 24(2): 24-26 HU C J, MA D K. Topological sequence entropy of some compact systems and generalized Specification property [J]. Journal of Guangdong University of Technology, 2007, 24(2): 24-26
[6] BIŚ A. Entropies of a semigroup of maps [J]. Discrete and Continuous Dynamical Systems, 2004, 11(2-3): 639-648
[7] BUFETOV A. Topological entropy of free semigroup actions and skew-product transformations [J]. Journal of Dynamical and Control Systems, 1999, 5(1): 137-143
[8] 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
[9] 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
[10] 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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