University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The Hausdorff dimension of not uniquely ergodic 4-IETs has codimension 1/2.

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

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Interactions between Dynamics of Group Actions and Number Theory

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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