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Theses

Empilements de sphères et bêta-entiers

Abstract : Sphere packings, mostly in R^n, and beta-integers, are the objects considered in this thesis. They are indifferently described in the language of sphere packings or in that of uniformly discrete sets. We have considered the following problems: (i) metrical and topological aspects of the space of sphere packings for which we prove a compactness theorem which generalizes the Selection Theorem of Mahler relative to lattices, (ii) relationships between deep holes and density via the Delone constant and the internal asymptotic structure, by layers, of densest sphere packings, (iii) self-similar sphere packings of finite type for which we show, for each of them, the existence of a cut-and-project scheme associated with an algebraic integer (the self-similarity) the degree of which divides the rank of the packing, in the context of mathematical quasicrystals, (iv) sphere packings on beta-lattices whose study was mainly devoted to the understanding of the locally finite discrete set Z_beta of beta-integers and to propose a new classification of algebraic numbers which is complementary to that of Bertrand-Mathis, reported in an article by Blanchard, and where the Mahler's measure plays a natural rôle.
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https://tel.archives-ouvertes.fr/tel-00083823
Contributor : Martine Barbelenet <>
Submitted on : Wednesday, July 19, 2006 - 3:24:32 PM
Last modification on : Monday, February 8, 2021 - 12:22:04 PM
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Jean-Louis Verger-Gaugry. Empilements de sphères et bêta-entiers. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2006. Français. ⟨tel-00083823⟩

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