Slowly divergent geodesics in moduli space
Author:
Yitwah Cheung
Journal:
Conform. Geom. Dyn. 8 (2004), 167189
MSC (2000):
Primary 37A45; Secondary 11J70
Published electronically:
November 17, 2004
MathSciNet review:
2122525
Fulltext PDF Free Access
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Abstract: Slowly divergent Teichmüller geodesics in the moduli space of Riemann surfaces of genus are constructed via cyclic branched covers of the torus. Nonergodic examples (i.e. geodesics whose defining quadratic differential has nonergodic vertical foliation) diverging to infinity at sublinear rates are constructed using a Diophantine condition. Examples with an arbitrarily slow prescribed rate of divergence are also exhibited.
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 Y. Cheung, Hausdorff dimension of the set of nonergodic directions, Ann. of Math. 158 (2003), 661678. MR 2018932
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 Y. Cheung and A. Eskin, in preparation.
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 K. Falconer, Fractal Geometry. Mathematical Foundations and Applications, John Wiley & Sons Ltd., Chichester, 1990. MR 1102677 (92j:28008)
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 H. Masur, Hausdorff dimension of the set of nonergodic foliations of a quadratic differential, Duke Math. J. 66 (1992), 387442. MR 1167101 (93f:30045)
 [Ma93]
 H. Masur, Logarithmic law for geodesics in moduli space, Contemp. Math. 150 (1993), 229245. MR 1234267 (94h:32038)
 [MMY]
 S. Marmi, P. Moussa, J.C. Yoccoz, On the cohomological equation for interval exchange maps, C. R. Math. Acad. Sci. Paris 336 (2003), no. 11, 941948. MR 1994599 (2004i:37003)
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 W. Veech, Strict ergodicity in zero dimensional dynamical systems and the KroneckerWeyl theorem mod 2, Trans. Amer. Math. Soc. 140 (1969), 134. MR 0240056 (39:1410)
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Additional Information
Yitwah Cheung
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 602082730
DOI:
http://dx.doi.org/10.1090/S1088417304001134
PII:
S 10884173(04)001134
Received by editor(s):
January 12, 2004
Received by editor(s) in revised form:
September 4, 2004
Published electronically:
November 17, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
