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Conformal Geometry and Dynamics

ISSN 1088-4173



Slowly divergent geodesics in moduli space

Author: Yitwah Cheung
Journal: Conform. Geom. Dyn. 8 (2004), 167-189
MSC (2000): Primary 37A45; Secondary 11J70
Published electronically: November 17, 2004
MathSciNet review: 2122525
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Abstract: Slowly divergent Teichmüller geodesics in the moduli space of Riemann surfaces of genus $g\geq 2$ 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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Additional Information

Yitwah Cheung
Affiliation: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208-2730

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.