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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The Hausdorff dimension of non-uniquely ergodic directions in $H(2)$ is almost everywhere $1/2$

Jayadev S Athreya and Jon Chaika

Geometry & Topology 19 (2015) 3537–3563
Abstract

We show that for almost every (with respect to Masur–Veech measure) translation surface ω (2), the set of angles θ [0,2π) such that eiθω has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) 1 2. We show this by proving that the Hausdorff codimension of the set of non-uniquely ergodic interval exchange transformations (IETs) in the Rauzy class of (4321) is also 1 2.

Keywords
interval exchange transformation, Hausdorff dimension, Rauzy induction
Mathematical Subject Classification 2010
Primary: 37E05, 37E35
References
Publication
Received: 14 September 2014
Revised: 13 January 2015
Accepted: 15 February 2015
Published: 6 January 2016
Proposed: Leonid Polterovich
Seconded: David Gabai, Yasha Eliashberg
Authors
Jayadev S Athreya
Department of Mathematics
University of Washington
Box 354350
Seattle, WA 98195-4350 USA
http://faculty.washington.edu/jathreya
Jon Chaika
Department of Mathematics
University of Utah
155 S 1400 E Room 233
Salt Lake City, UT 84112-0090
USA
http://www.math.utah.edu/~chaika