Refined shrinking target property of rotations

초록

In this study we discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational theta and monotonically increasing phi(n) such that lim (n -> infinity) inf n phi(n) parallel to n theta - s parallel to = 0 for almost every s. We also consider the class of irrationals for which the limit inferior is 0 for every monotonically increasing phi(n) such that Sigma(n) 1/(n phi(n)) diverges.

키워드