On the closedness of approximation spectra

2008/06/02 by Jouni Parkkonen, Parkkonen, Jouni, Frédéric Paulin +1
Mathematics · #11J06 #53C22 #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.DG #math.NT #msc:11J06 #msc:53C22

paper · pdf · doi:10.48550/arxiv.0806.0304

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

openalex publication_date 2008/06/02 · arxiv created 2010/01/07 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Arithmetic Subgroups of Algebraic Groups

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