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Topological pressure for an iterated function system
Dynamical Systems ( IF 0.5 ) Pub Date : 2021-06-03 , DOI: 10.1080/14689367.2021.1929081
Huoyun Wang 1 , Xing Liao 1
Affiliation  

In this paper, we introduce a notion of topological pressure, which is different from the LMW's and ML's for an iterated function system. We find out the properties of the topological pressure, which are more similar to the properties of the classical topological pressure than LMW's and ML's. For an iterated function system, we obtain a partial variational principle on topological pressure, which improves the LMW's related result. Finally, we give a lower bound estimation of the topological pressure for a Ruelle-expanding iterated function system. In particular, we point out the exponential growth rate of fixed points is a lower bound of WLLZ's topological entropy for a Ruelle-expanding iterated function system.



中文翻译:

迭代函数系统的拓扑压力

在本文中,我们引入了拓扑压力的概念,它不同于迭代函数系统的 LMW 和 ML。我们发现了拓扑压力的性质,它比 LMW 和 ML 更类似于经典拓扑压力的性质。对于迭代函数系统,我们得到了拓扑压力的偏变分原理,改进了LMW的相关结果。最后,我们给出了一个 Ruelle 扩展迭代函数系统的拓扑压力的下界估计。特别地,我们指出不动点的指数增长率是 Ruelle 扩展迭代函数系统的 WLLZ 拓扑熵的下界。

更新日期:2021-06-03
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