CRM: Centro De Giorgi
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Seminari di Sistemi Dinamici Olomorfi 2011-2012

seminar: The dimension set of recurrence of the irrational rotation

speaker: Dong Han Kim (Dongguk University)

abstract: We study the hitting time of the irrational rotations. Let \(\tau_r(x,y)\) be the first time for \(x\) to hit the ball of center \(y\) and radius \(r\). We study the limit behavior of \(\frac{\log \tau_r(x,y)}{-\log r}\). The lower limit concerns the existence of infinite solutions of some Diophantine equations, which is widely studied in the literature, while the upper limit is related to the Uniform Dirichlet's theorem, i.e., for any given number \(Q\geq 1\), the existence of solution less than \(Q\) of Diophantine equations. In this paper we mainly study the upper limit. The Hausdorff dimensions of the sets of level sets of the upper limit are estimated.
[This a joint work with Lingmin Liao]


timetable:
Thu 26 Jan, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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