On circle rotations and the shrinking target properties
Dynamical Systems
2007-10-09 v2 Number Theory
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.
Cite
@article{arxiv.math/0702853,
title = {On circle rotations and the shrinking target properties},
author = {Jimmy Tseng},
journal= {arXiv preprint arXiv:math/0702853},
year = {2007}
}
Comments
13 pages. A new section has been added. The rest of the paper remains the same except for some very minor revisions.