CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2013-2014

seminar: On the refined shrinking target property of rotations

speaker: Dong Han Kim (Dongguk University)

abstract: We discuss the shrinking target property of irrational rotations. Suppose that $varphi(n)$ is a monotone increasing function such that $sumn 1(nvarphi(n))$ diverges. We obtain the condition of an irrational $theta$ and monotone increasing $varphi(n)$ such that $$ liminf{n to infty} n varphi (n)
ntheta - s
= 0 text{ for almost every } s. $$ We also consider the class of irrationals for which the limit inferior is 0 for every monotone increasing $varphi(n)$ such that $sumn 1
(nvarphi(n))$ diverges.

Tue 4 Feb, 11:00 - 12:00, Sala Conferenze Centro De Giorgi
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