Dimension de Hausdorff. Application aux nombres normaux
Dimension de Hausdorff de certains fractals aléatoires
On construit des ensembles de Cantor aléatoires par partages successifs de rectangles, en partant d’un carré, (le nombre de divisions de la longueur peut être différent de celui de la largeur). La construction est stationnaire : elle fait intervenir des variables aléatoires indépendantes et équidistribuées. Sur ces ensembles il existe une mesure naturelle, , aléatoire elle aussi. Des résultats concernant les boréliens portant et leur dimension de Hausdorff ont déjà été obtenus par J. Peyrière...
Dimension d'ensembles plans définis par des propriétés des développements des coordonnées
Dimension des courbes planes, papiers plies et suites de Rudin-Shapiro
Dimension of countable intersections of some sets arising in expansions in non-integer bases
We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.
Dimensions des spirales
Dimensions of anisotropic indefinite quadratic forms. I.
Dimensions of anisotropic indefinite quadratic forms. II.
Dimensions of some affine Deligne–Lusztig varieties
Dimensions of spaces of cusp forms over function fields.
Dimensions of spaces of modular forms for
Diophantine Analysis Applied to Virus Structure.
Diophantine approximation and certain sequences of lattices
Diophantine approximation and deformation
Diophantine Approximation and Lattices with Complex Multiplication.
Diophantine approximation and special Liouville numbers
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers . The approach relies on results on the connection between the set of all -adic expansions () of and their associated approximation constants. As an application, explicit construction of real numbers with prescribed approximation properties are deduced and illustrated by Matlab plots.
Diophantine approximation by square-free numbers
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Diophantine approximation in Banach spaces
In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.
Diophantine Approximation in certain Solenoids