Journal of Guangdong University of Technology ›› 2020, Vol. 37 ›› Issue (03): 59-62.doi: 10.12052/gdutxb.190126

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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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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

CLC Number: 

  • O189.1
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