3 papers
math.DS2005
Slowly divergent geodesics in moduli space
Y. Cheung
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…
math.DS2005
Minimal nonergodic directions on genus 2 translation surfaces
Y. Cheung, H. Masur
It is well-known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus 2 translation surface which is n…
math.DS2004
Hausdorff dimension of the set of nonergodic directions (with an appendix by M. Boshernitzan)
Yitwah Cheung
It is known that nonergodic directions in a rational billiard form a subset of the unit circle with Hausdorff dimension at most 1/2. Explicit examples realizing the dimension 1/2 a…