Slowly divergent geodesics in moduli space

Details Slowly divergent geodesics in moduli space Slowly divergent geodesics in moduli space

2005-01-19

arxiv.org/abs/math/0501295v1

Conformal Geometry & Dynamics. 8 (2004) 167-189

Mathematics

Dynamical Systems

26 pages, no figures

Scientific paper

Slowly divergent geodesics in the moduli space of Riemann surfaces of genus at least 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 growth rate are also exhibited.

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