Mathematics Department Colloquium
Spring 2005

Date: Thursday, March 31
Time: 4:00 p.m.
Location: 215 Thomas Building
Name: Sheldon Newhouse
Affiliation: Michigan State University
Title: Cantor Sets, Continued Fractions, and Dynamics on Surfaces

Abstract: There are many mathematical instances in which Cantor sets naturally arise. Also, in many cases, the "sizes" of the Cantor sets have different implications. We discuss several of these situations, from an old theorem of Marshall Hall about representations of positive reals as sums of restricted continued fractions to the existence of invariant sets of full Hausdorff dimension for surface diffeomorphisms and implications for the "symbolic representation" of typical surface diffeomorphisms.