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The
Hausdorff dimension of non-uniquely ergodic directions in
$H(2)$ is almost everywhere $1/2$
Jayadev S Athreya and Jon Chaika |
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Geometry & Topology 19 (2015) 3537–3563
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Abstract |
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We show that for almost every (with respect to Masur–Veech measure) translation surface , the set of angles such that has non-uniquely ergodic vertical foliation has Hausdorff dimension (and codimension) . 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 is also . |
Keywords
interval exchange transformation, Hausdorff dimension,
Rauzy induction
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Mathematical Subject Classification 2010
Primary: 37E05, 37E35
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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
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Authors |
| Jayadev S Athreya | |
| Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350 USA |
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| 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 |
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| http://www.math.utah.edu/~chaika | |
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