On the closedness of approximation spectra

Details On the closedness of approximation spectra On the closedness of approximation spectra

2008-06-02

arxiv.org/abs/0806.0304v2

Mathematics

Number Theory

Revised version. To appear in J. Theor. Nombres Bordeaux

Scientific paper

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.

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