Slowly divergent geodesics in moduli space

Cheung, Yitwah

doi:10.1090/S1088-4173-04-00113-4

Slowly divergent geodesics in moduli space
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by Yitwah Cheung

Conform. Geom. Dyn. 8 (2004), 167-189

DOI: https://doi.org/10.1090/S1088-4173-04-00113-4

Published electronically: November 17, 2004

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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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