Shrinking targets for IETs: Extending a theorem of Kurzweil

الأصل · EN

This paper proves shrinking target results for IETs. Let a₁≥ a₂ ≥... be a sequence of positive real numbers with divergent sum. Then for almost every IET T, the limsup of B(Tⁱx,aᵢ) 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.