Y. Cheung
Published 2005-01-19Version 1
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.
Comments: 26 pages, no figures
Journal: Conformal Geometry & Dynamics. 8 (2004) 167-189
Bounded geodesics in moduli space
Limiting distribution of lattice orbits in a moduli space of rank 2 discrete subgroups in 3-space
Limiting distribution of dense orbits in a moduli space of rank $m$ discrete subgroups in $(m+1)$-space
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