关于旋转的加细缩靶性质
On the refined shrinking target property of rotations
摘要：
讨论了无理旋转的缩靶性质。我们得到了无理数$θ$和单调递增$φ(n)$使得$$ \liminf_{n \to \infty} n φ(n) \| nθ- s \| = 0 \text{ for almost every } s. $$的条件。我们还考虑了对每个单调递增$φ(n)$下极限为0使得$\sum_n 1/(nφ(n))$发散的无理数类。
英文摘要：
We discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational $θ$ and monotone increasing $φ(n)$ such that $$ \liminf_{n \to \infty} n φ(n) \| nθ- s \| = 0 \text{ for almost every } s. $$ We also consider the class of irrationals for which the limit inferior is 0 for every monotone increasing $φ(n)$ such that $\sum_n 1/(nφ(n))$ diverges.
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