Shrinking targets for IETs: Extending a theorem of Kurzweil

Details Shrinking targets for IETs: Extending a theorem of Kurzweil Shrinking targets for IETs: Extending a theorem of Kurzweil

2009-10-14

arxiv.org/abs/0910.2694v2

Mathematics

Dynamical Systems

22 pages. Substantially revised

Scientific paper

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.

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