• Corpus ID: 239016375

The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds

@inproceedings{Beck2020TheKE,
  title={The Kronecker-Weyl equidistribution theorem and geodesics in 3-manifolds},
  author={J{\'o}zsef Beck and William W. L. Chen},
  year={2020}
}
Given any rectangular polyhedron 3-manifold P tiled with unit cubes, we find infinitely many explicit directions related to cubic algebraic numbers such that all half-infinite geodesics in these directions are uniformly distributed in P. 

References

SHOWING 1-10 OF 18 REFERENCES
Billiards on almost integrable polyhedral surfaces
The phase space of the geodesic flow on an almost integrable polyhedral surface is foliated into a one-parameter family of invariant surfaces. The flow on a typical invariant surface is minimal. We
Flat Surfaces
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a
Introduction to Diophantine Approximation
TLDR
This article formalizes some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals and proves that the inequality |xθ − y| ≤ 1/x has infinitely many solutions by continued fractions.
Quantitative behavior of non-integrable systems. I
The theory of Uniform Distribution started with the equidistribution of the irrational rotation of the circle, proved around 1905 independently by Bohl, Sierpinski and Weyl. The quantitative
Recurrence in Ergodic Theory and Combinatorial Number Theory
TLDR
The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press, to preserve the original texts of these important books while presenting them in durable paperback editions.
Über die Gleichverteilung von Zahlen mod. Eins
----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung
Quantitative behavior of non-integrable systems (III)
The main purpose of the paper is to give explicit geodesics and billiard orbits in polysquares and polycubes that exhibit time-quantitative density. In many instances of the 2-dimensional case
An introduction to Veech surfaces
  • Handbook of Dynamical Systems (B. Hasselblatt, A. Katok, eds.), volume
  • 2006
An introduction to Veech surfaces. Handbook of Dynamical Systems
  • 2006
...
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