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Quantitative recurrence properties in the historic set for symbolic systems
Dynamical Systems ( IF 0.5 ) Pub Date : 2020-12-10 , DOI: 10.1080/14689367.2020.1855416
Cao Zhao 1
Affiliation  

Let (ΣA,σ) be a topologically mixing subshift of finite type on an alphabet consisting of m symbols. Let φ:ΣAR be a continuous function. For a positive function ψ:NR+ and a continuous positive function f:ΣAR+, define the sets of recurrence points R(ψ,φ):={xΣA:d(σnx,x)<ψ(n)for infinitely many n andlimn1ni=0n1φ(σix)does not exist}and R(f,φ):={xΣA:d(σnx,x)<eSnf(x)for infinitely many n andlimn1ni=0n1φ(σix) does not exist }.In this paper, we give quantitative estimates of the sets of recurrence points, that is, dimHR(ψ,φ) can be expressed by ψ and dimHR(f,φ) is the solution of the Bowen equation of topological pressure.



中文翻译:

符号系统历史集中的定量递归性质

(Σ一种,σ)是由m 个符号组成的字母表上的有限类型的拓扑混合子位移。让φΣ一种电阻是连续函数。对于正函数ψN电阻+ 和一个连续的正函数 FΣ一种电阻+, 定义重复点集 电阻(ψ,φ):={XΣ一种d(σnX,X)<ψ(n)对于无限多 n 和n1n一世=0n-1φ(σ一世X)不存在}电阻(F,φ):={XΣ一种d(σnX,X)<电子-nF(X)对于无限多 n 和n1n一世=0n-1φ(σ一世X) 不存在 }在本文中,我们给出了重复点集的定量估计,即, 暗淡H电阻(ψ,φ)可以用ψ暗淡H电阻(F,φ)是拓扑压力的鲍文方程的解。

更新日期:2020-12-10
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