4 papers · 1 filter
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…
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…
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…
Generalization of a density theorem of Khinchin and diophantine approximation
J. Beck, W. W. L. Chen
The continuous version of a fundamental result of Khinchin says that a half-infinite torus line in the unit square exhibits superdensity, which is a best form of time-qua…