We investigate, for a given time $T$, the measure of the set of $\Gamma$-equivalent classes of geodesics with distance at most $N(T)$ from a sufficiently large fixed compact subset $D$ of $\Gamma\backslash\mathcal{T}$ up to time $T$. We show that there exists a function $N(T)$ such that for Bowen–Margulis measure $\mu$ on the space $\Gamma\backslash\mathcal{GT}$ of geodesics and the critical exponent $\delta$ of $\Gamma$, $$\lim_{T\to\infty}\mu(\{[l]\in\Gamma\backslash\mathcal{GT}\colon \underset{0\le t \le T}{\textrm{max}}d(D,l(t))\le N(T)+y\})=e^{-q^y/e^{2\delta y}}.$$ In fact, we obtain a precise formula for $N(T)$: there exists a constant $C$ depending on $\Gamma$ and $D$ such that $$N(T)=\log_{e^{2\delta/q}}\Big(\frac{T(e^{2\delta-q)}}{2e^{2\delta}-C(e^{2\delta}-q)}\Big).$$

对于给定的时间$ T $，我们调查距离足够大的$ \ Gamma的固定紧致子集$ D $距离为$ N（T）$的，与$ \ Gamma $等价的测地线集合的度量\ backslash \ mathcal {T} $到$ T $。我们证明存在一个函数$ N（T）$，对于Bowen–Margulis，在测地线$ \ Gamma \反斜杠\ mathcal {GT} $和$的临界指数$ \ delta $上测量$ \ mu $ \ Gamma $，$$ \ lim_ {T \ to \ infty} \ mu（\ {[l] \ in \ Gamma \反斜杠\数学{GT} \冒号\底线{0 \ le t \ le T} {\ textrm {max}} d（D，l（t））\ le N（T）+ y \}）= e ^ {-q ^ y / e ^ {2 \ delta y}}。$$实际上，我们得到$ N（T）$的精确公式：存在取决于$ \ Gamma $和$ D $的常数$ C $，使得$$ N（T）= \ log_ {e ^ {2 \ delta / q}} \ Big（\ frac {T（e ^ {2 \ delta-q）}} {2e ^ {2 \ delta} -C（e ^ {2 \ delta} -q）} \ Big）。$$