7 papers
A note on the Kronecker--Weyl equidistribution theorem
J. Beck, W. W. L. Chen, Y. Yang
We study the relationship between the discrete and the continuous versions of the Kronecker--Weyl equidistribution theorem, as well as their possible extension to manifolds in high…
Irreversible and dissipative systems
J. Beck, W. W. L. Chen, Y. Yang
We study some new dynamical systems where the corresponding piecewise linear flow is neither time reversible nor measure preserving. We create a dissipative system by starting with…
A note on density of geodesics
J. Beck, W. W. L. Chen, Y. Yang
We extend the famous result of Katok and Zemlyakov on the density of half-infinite geodesics on finite flat rational surfaces to half-infinite geodesics on a finite polycube transl…
Uniformity of geodesic flow in non-integrable 3-manifolds
J. Beck, W. W. L. Chen, Y. Yang
Almost nothing is known concerning the extension of -dimensional Kronecker--Weyl equidistribution theorem on geodesic flow from the unit torus to non-integrable finite…
Billiards in polyhedra: a method to convert 2-dimensional uniformity to 3-dimensional uniformity
J. Beck, W. W. L. Chen, Y. Yang
The class of 2-dimensional non-integrable flat dynamical systems has a rather extensive literature with many deep results, but the methods developed for this type of problems, both…
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…