Slowly divergent geodesics in moduli space
Dynamical Systems
2007-05-23 v1 Number Theory
Abstract
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.
Cite
@article{arxiv.math/0501295,
title = {Slowly divergent geodesics in moduli space},
author = {Y. Cheung},
journal= {arXiv preprint arXiv:math/0501295},
year = {2007}
}
Comments
26 pages, no figures