次可加拓扑压变分原理的另一证明

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 977-982.

次可加拓扑压变分原理的另一证明

徐兰()

^{苏州市职业大学数理部江苏苏州 215104}

收稿日期:2019-04-19 出版日期:2020-08-26 发布日期:2020-08-20
作者简介:徐兰, E-mail:xlan@jssvc.edu.cn
基金资助:
国家自然科学基金(11871361)

Another Proof of Variational Principle for Sub-Additive Potentials

Lan Xu()

^{Department of Mathematics and Physics, Suzhou Vocational University, Jiangsu Suzhou 215104}

Received:2019-04-19 Online:2020-08-26 Published:2020-08-20
Supported by:
the NSFC(11871361)

摘要/Abstract

摘要：

对拓扑动力系统$(X, T)$,当势函数为次可加函数序列时，拓扑压的变分原理成立.次可加拓扑压的变分原理在研究自仿集和非共形排斥子的平衡态及维数估计中具有非常重要的作用，且在目前为止，所有的应用都集中在可扩系统情形.事实上，可扩系统的熵映射都是上半连续的，论文给出了熵映射上半连续时次可加拓扑压变分原理的一个简单证明.

关键词: 拓扑压, 次可加势函数, 变分原理

Abstract:

The variational principle of topological pressure for sub-additive potentials was proved by Cao etal. This generalized variational principle plays an important role in the theory of dimension and equilibrium state for some expansive dynamical systems such as, for example, self-affine fractals and non-conformal repellers. The main purpose of this paper is to give another proof for the variational principle in the sub-additive case when the entropy map is upper semi-continuous.

Key words: Topological Pressure, Sub-additive Potential, Variational Principle

中图分类号:

O193

徐兰. 次可加拓扑压变分原理的另一证明[J]. 数学物理学报, 2020, 40(4): 977-982.

Lan Xu. Another Proof of Variational Principle for Sub-Additive Potentials[J]. Acta mathematica scientia,Series A, 2020, 40(4): 977-982.

参考文献 12

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