Let $({\mathrm{\Sigma }}_A,\sigma )$ be a topologically mixing subshift of finite type on an alphabet consisting of m symbols. Let $\phi :{\mathrm{\Sigma }}_A\to \mathbb{R}$ be a continuous function. For a positive function $\psi :\mathbb{N}\to {\mathbb{R}}^{+}$ and a continuous positive function $f:{\mathrm{\Sigma }}_A\to {\mathbb{R}}^{+}$, define the sets of recurrence points $\begin{array}{rl}R(\psi ,\phi )& :=\{x\in {\mathrm{\Sigma }}_A:d({\sigma }^{n}x,x)<\psi (n)\text{for infinitely many }n\text{ and}\\ & \underset{n\to \mathrm{\infty }}{lim}\frac{1}{n}\sum _{i=0}^{n-1}\phi ({\sigma }^{i}x)\text{does not exist}\}\end{array}$and $\begin{array}{rl}R(f,\phi )& :=\{x\in {\mathrm{\Sigma }}_A:d({\sigma }^{n}x,x)<e^{-S_{n}f(x)}\text{for infinitely many }n\text{ and}\\ & \underset{n\to \mathrm{\infty }}{lim}\frac{1}{n}\sum _{i=0}^{n-1}\phi ({\sigma }^{i}x)\text{ does not exist }\}.\end{array}$In this paper, we give quantitative estimates of the sets of recurrence points, that is, ${\dim }_{H}R(\psi ,\phi )$ can be expressed by ψ and ${\dim }_{H}R(f,\phi )$ is the solution of the Bowen equation of topological pressure.

让 $({\mathrm{\Sigma }}_{\mathrm{一种}},\sigma )$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$\phi ：{\mathrm{\Sigma }}_{\mathrm{一种}}\to \mathbb{电阻}$是连续函数。对于正函数$\psi ：\mathbb{N}\to {\mathbb{电阻}}^{+}$ 和一个连续的正函数 $F：{\mathrm{\Sigma }}_{\mathrm{一种}}\to {\mathbb{电阻}}^{+}$, 定义重复点集 $\begin{array}{rl}\mathrm{电阻}(\psi ,\phi )& :=\{X\in {\mathrm{\Sigma }}_{\mathrm{一种}}：d({\sigma }^{n}X,X)<\psi (n)\text{对于无限多 }n\text{ 和}\\ & \underset{n\to \mathrm{\infty }}{林}\frac{1}{n}\sum _{\mathrm{一世}=0}^{n-1}\phi ({\sigma }^{\mathrm{一世}}X)\text{不存在}\}\end{array}$和 $\begin{array}{rl}\mathrm{电阻}(F,\phi )& :=\{X\in {\mathrm{\Sigma }}_{\mathrm{一种}}：d({\sigma }^{n}X,X)<{\mathrm{电子}}^{-{秒}_{n}F(X)}\text{对于无限多 }n\text{ 和}\\ & \underset{n\to \mathrm{\infty }}{林}\frac{1}{n}\sum _{\mathrm{一世}=0}^{n-1}\phi ({\sigma }^{\mathrm{一世}}X)\text{ 不存在 }\}。\end{array}$在本文中，我们给出了重复点集的定量估计，即， ${\mathrm{暗淡}}_H\mathrm{电阻}(\psi ,\phi )$可以用ψ和${\mathrm{暗淡}}_H\mathrm{电阻}(F,\phi )$是拓扑压力的鲍文方程的解。