Badly approximable numbers, Kronecker’s theorem, and diversity of Sturmian characteristic sequences
Badly approximable numbers, Kronecker’s theorem, and diversity of Sturmian characteristic sequences
We give an optimal version of the classical “three-gap theorem” on the fractional parts of nθ, in the case where θ is an irrational number that is badly approximable. As a consequence, we deduce a version of Kronecker’s inhomogeneous approximation theorem in one dimension for badly approximable numbers. We apply …