论文标题
最终总是达到积分
On eventually always hitting points
论文作者
论文摘要
我们考虑动态系统$（x，t，μ）$，它们具有Hölder连续函数或有限变化功能的相关性衰减。给定一系列球$（b_n）_ {n = 1}^\ infty $，我们为最终始终击中点的一组量提供了足够的条件。这是一组点$ x $，因此对于所有足够大的$ m $，在b_m $中有$ k <m $，带有$ t^k（x）\。我们还将$ m \至\ infty $在$ k <m $中给出$ m \ t^k（x）\ in b_m $中的$ m \ to \ infty $。作为一个应用程序，我们几乎在每个点$ x $ a in y x $ a insptotic估算上的$ k \ leq m $的数量是$ a_k \ geq m^t $，其中$ t \ in（0,1）$和$ a_k $是$ x $的持续分数系数。
We consider dynamical systems $(X,T,μ)$ which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls $(B_n)_{n=1}^\infty$, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points $x$ such that for all large enough $m$, there is a $k < m$ with $T^k (x) \in B_m$. We also give an asymptotic estimate as $m \to \infty$ on the number of $k < m$ with $T^k (x) \in B_m$. As an application, we prove for almost every point $x$ an asymptotic estimate on the number of $k \leq m$ such that $a_k \geq m^t$, where $t \in (0,1)$ and $a_k$ are the continued fraction coefficients of $x$.
