On the closedness of approximation spectra
Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, p. 703-712

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 [Mau].

Le spectre classique de Lagrange pour l’approximation des nombres réels par des rationnels, est fermé, par un théorème de Cusick. Plus généralement, nous montrons que de nombreux spectres d’approximation sont fermés, en utilisant des propriétés de pénétration du flot géodésique dans des voisinages de pointes de variétés à courbure strictement négative, et un résultat de Maucourant [Mau].

@article{JTNB_2009__21_3_703_0,
     author = {Parkkonen, Jouni and Paulin, Fr\'ed\'eric},
     title = {On the closedness of approximation spectra},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {21},
     number = {3},
     year = {2009},
     pages = {703-712},
     doi = {10.5802/jtnb.696},
     mrnumber = {2605541},
     zbl = {1205.11083},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2009__21_3_703_0}
}
Parkkonen, Jouni; Paulin, Frédéric. On the closedness of approximation spectra. Journal de théorie des nombres de Bordeaux, Volume 21 (2009) no. 3, pp. 703-712. doi : 10.5802/jtnb.696. http://www.numdam.org/item/JTNB_2009__21_3_703_0/

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