Yitwah Cheung

Topological dichotomy and strict ergodicity for translation surfaces

In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction either the flow in that direction is completely periodic or minimal, and yet have minimal but non uniquely ergodic directions.

A divergent teichmüller geodesic with uniquely ergodic vertical foliation

We construct an example of a quadratic differential whose vertical foliation is uniquely ergodic and such that the Teichmüller geodesic determined by the quadratic differential diverges in the moduli space of Riemann surfaces.

Minimal non-ergodic directions on genus-2 translation surfaces

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 not a Veech surface there are uncountably many minimal but not uniquely ergodic directions. The theorem can be applied to certain billiard tables.

Hausdorff dimension of the set of points on divergent trajectories of a homogeneous flow on a product space

In this paper we compute the Hausdorff dimension of the set

Hausdorff dimension of singular vectors

D(\varphi_n)

Slowly divergent geodesics in moduli space

of points on divergent trajectories of the homogeneous flow

Piecewise isometries, uniform distribution and 3log 2-pi2/8

\varphi_n

Hausdorff dimension of the set of nonergodic directions

induced by the one-parameter subgroup

Hausdorff dimension of the set of singular pairs

\mathop{\rm diag}(e^t,e^{-t})

Dichotomy for the Hausdorff dimension of the set of nonergodic directions

acting by left multiplication on the product space