4 papers · 1 filter
Uniformity in cube-covering systems
J. Beck, W. W. L. Chen
We establish various analogs of the Kronecker-Weyl equidistribution theorem that can be considered higher-dimensional versions of results established in our earlier investigation o…
Superdensity and super-micro-uniformity in non-integrable flat systems
J. Beck, W. W. L. Chen
We show that on any non-integrable finite polysquare translation surface, superdensity, an optimal form of time-quantitative density, leads to an optimal form of time-quantitative…
Super-fast spreading of billiard orbits in rational polygons and geodesics on translation surfaces
J. Beck, W. W. L. Chen
In this paper, we show that billiard orbits in rational polygons and geodesics on translation surfaces exhibit super-fast spreading, an optimal time-quantitative majority property…
Time-quantitative density of non-integrable systems
J. Beck, W. W. L. Chen
We introduce a new method to establish time-quantitative density in flat dynamical systems. First we give a shorter and different proof of our earlier result that a half-infinite g…