论文标题
关于缩小的目标和自我撤回点
On shrinking targets and self-returning points
论文作者
论文摘要
我们考虑集合$ \ mathcal {r} _ \ mathrm {io} $的积分，这些点无限地返回到一系列自身周围的缩小目标。在其他假设下，我们改善了Boshernitzan的开创性速度，会导致复发的速度。在二倍地图以及$ d $尺寸圆环上的一些线性地图的情况下，我们甚至获得了$ \ mathcal {r} _ \ mathrm {io} $的二分法条件，以使零或一个。此外，我们研究了一组最终始终返回的要点，并证明了Boshernitzan具有类似一般性的结果。
We consider the set $\mathcal{R}_\mathrm{io}$ of points returning infinitely many times to a sequence of shrinking targets around themselves. Under additional assumptions we improve Boshernitzan's pioneering result on the speed of recurrence. In the case of the doubling map as well as some linear maps on the $d$ dimensional torus, we even obtain a dichotomy condition for $\mathcal{R}_\mathrm{io}$ to have measure zero or one. Moreover, we study the set of points eventually always returning and prove an analogue of Boshernitzan's result in similar generality.
