On circle rotations and the shrinking target properties
arXiv:math/0702853
Abstract
We generalize the monotone shrinking target property (MSTP) to the s-exponent monotone shrinking target property (sMSTP) and give a necessary and sufficient condition for a circle rotation to have sMSTP. Using another variant of MSTP, we obtain a new, very short, proof of a known result, which concerns the behavior of irrational rotations and implies a logarithm law similar to D. Sullivan's logarithm law for geodesics.
13 pages. A new section has been added. The rest of the paper remains the same except for some very minor revisions.