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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Twisted Diophantine approximation and shrinking targets
by
Simon Kristensen
University of Aarhus
Coauthors: Yann Bugeaud (Strasbourg), Stephen Harrap (York), Sanju Velani (York)

Consider an irrational rotation of the circle. It is well-known that the orbits of such a rotation are dense. This density can be made quantitative using the notion of shrinking targets. We consider the set of points which a given orbit tries to stay away from. This set can be described in terms of so-called twisted inhomogeneous Diophantine approximation. We show that the set is large in terms of Hausdorff dimension. Higher dimensional analogues are also described.

Date received: June 13, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-87.