208 citations · 302 across the 13 of their papers we have counts for
13 papers
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…
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…
Quantitative behavior of non-integrable systems (IV)
Jozsef Beck, William Chen, Yuxuan Yang
In this paper, there are two sections. In Section 7, we simplify the eigenvalue-based surplus shortline method for arbitrary finite polysquare translation surfaces. This makes it s…
Quantitative behavior of non-integrable systems (III)
J. Beck, W. W. L. Chen, Y. Yang
The main purpose of part (III) is to give explicit geodesics and billiard orbits in polysquares that exhibit time-quantitative density. In many instances, we can even establish a b…