On the closedness of approximation spectra
Number Theory
2010-01-07 v2 Differential Geometry
Abstract
Generalizing Cusick's theorem on the closedness of the classical Lagrange spectrum for the approximation of real numbers by rational ones, we prove that various approximation spectra are closed, using penetration properties of the geodesic flow in cusp neighbourhoods in negatively curved manifolds and a result of Maucourant.
Cite
@article{arxiv.0806.0304,
title = {On the closedness of approximation spectra},
author = {Jouni Parkkonen and Frédéric Paulin},
journal= {arXiv preprint arXiv:0806.0304},
year = {2010}
}
Comments
Revised version. To appear in J. Theor. Nombres Bordeaux