Shrinking targets for IETs: Extending a theorem of Kurzweil
Dynamical Systems
2011-04-13 v2 Number Theory
Abstract
This paper proves shrinking target results for IETs. Let {a_1\geq a_2 \geq...} be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(T^ix,a_i) has full Lebesgue measure (where B(z, e) is the open ball around z of radius e). Related results are established including the analogous result for geodesic flows on a translation surface.
Keywords
Cite
@article{arxiv.0910.2694,
title = {Shrinking targets for IETs: Extending a theorem of Kurzweil},
author = {Jon Chaika},
journal= {arXiv preprint arXiv:0910.2694},
year = {2011}
}
Comments
22 pages. Substantially revised