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

2020/12/17 by Beck, Jozsef, Chen, William
#11K38 #37E35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2012.09464

Abstract

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.

Related

• Uniformity of geodesic flow in non-integrable 3-manifolds
• Uniformity in cube-covering systems
• A note on density of geodesics
• A note on the Kronecker--Weyl equidistribution theorem
• New Kronecker-Weyl type equidistribution results and diophantine approximation