Diophantine Numbers in Dynamics
Time and place
12 PM on Thursday, March 19th, 2009; NAC 6/113
Dr. Yitwah Cheung (San Francisco State University)
Abstract
Irrational numbers may be classified in terms of how well they can be approximated by rationals. On one end of the spectrum we have "badly approximable" numbers, which includes all quadratic irrationals (the golden mean, in particular) while on the other end we have Liouville numbers, which are named after the mathematician who first used them to construct examples of transcendental numbers. In this talk I will describe how these notions arise naturally in the study of rational billiards. I will also explain how dynamical systems can be used to study properties of numbers, and if time permits, I will mention some recent progress in theory of simultaneous Diophantine approximation.
