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The Hausdorff dimension of not uniquely ergodic 4-IETs has codimension 1/2.

Presented by: 
J Chaika University of Utah
Date: 
Tuesday 1st July 2014 - 09:00 to 09:50
Venue: 
INI Seminar Room 1
Abstract: 
The main results of this talk are: a) The Hausdorff dimension of not-uniquely 4-IETs is 2 1/2 as a subset of the 3 dimensional simplex b) The Hausdorff dimension of flat surfaces in H(2) whose vertical flow is not uniquely ergodic is 7 1/2 as a subset of an 8 dimensional space c) For almost every flat surface in H(2) the set of directions where the flow is not uniquely ergodic has Hausdorff dimension 1/2. These results all say that the Hausdorff codimension of these exceptional sets is 1/2. Masur-Smillie showed that the Hausdorff codimension was less than 1. It follows from work of Masur that the Hausdorff codimension is at least 1/2. This is joint work with J. Athreya.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons