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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

Geometry & Topology 19 (2015) 3537–3563
Bibliography
1 Y Cheung, Hausdorff dimension of the set of nonergodic directions, Ann. of Math. 158 (2003) 661 MR2018932
2 Y Cheung, P Hubert, H Masur, Dichotomy for the Hausdorff dimension of the set of nonergodic directions, Invent. Math. 183 (2011) 337 MR2772084
3 M Keane, Non-ergodic interval exchange transformations, Israel J. Math. 26 (1977) 188 MR0435353
4 S Kerckhoff, H Masur, J Smillie, Ergodicity of billiard flows and quadratic differentials, Ann. of Math. 124 (1986) 293 MR855297
5 H B Keynes, D Newton, A “minimal”, non-uniquely ergodic interval exchange transformation, Math. Z. 148 (1976) 101 MR0409766
6 M Kontsevich, A Zorich, Connected components of the moduli spaces of Abelian differentials with prescribed singularities, Invent. Math. 153 (2003) 631 MR2000471
7 H Masur, Interval exchange transformations and measured foliations, Ann. of Math. 115 (1982) 169 MR644018
8 H Masur, Hausdorff dimension of the set of nonergodic foliations of a quadratic differential, Duke Math. J. 66 (1992) 387 MR1167101
9 H Masur, J Smillie, Hausdorff dimension of sets of nonergodic measured foliations, Ann. of Math. 134 (1991) 455 MR1135877
10 P Mattila, Geometry of sets and measures in Euclidean spaces: fractals and rectifiability, Cambridge Stud. Adv. Math. 44, Cambridge Univ. Press (1995) MR1333890
11 Y Minsky, B Weiss, Cohomology classes represented by measured foliations, and Mahler's question for interval exchanges, Ann. Sci. Éc. Norm. Supér. 47 (2014) 245 MR3215923
12 E A Sataev, The number of invariant measures for flows on orientable surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975) 860 MR0391184
13 W A Veech, A Kronecker–Weyl theorem modulo $2$, Proc. Nat. Acad. Sci. USA 60 (1968) 1163 MR0231795
14 W A Veech, Interval exchange transformations, J. Analyse Math. 33 (1978) 222 MR516048
15 W A Veech, Gauss measures for transformations on the space of interval exchange maps, Ann. of Math. 115 (1982) 201 MR644019
16 J C Yoccoz, Continued fraction algorithms for interval exchange maps: An introduction, from: "Frontiers in number theory, physics, and geometry, I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 401 MR2261103
17 A Zorich, Flat surfaces, from: "Frontiers in number theory, physics, and geometry, I" (editors P Cartier, B Julia, P Moussa, P Vanhove), Springer (2006) 437 MR2261104