Seminari di Sistemi Dinamici Olomorfi 2011-2012
timetable:
Thu 26 Jan, 15:00 - 16:00, Sala Conferenze Centro De Giorgi
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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
<< Go back