Shrinking targets for IETs: Extending a theorem of Kurzweil

Jon Chaika

Published 2009-10-14, updated 2011-04-11Version 2

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.