Das Hausdorff-Maß von Cantormengen.
Die Hausdorff-Dimension von Mengen reeller Zahlenfolgen.
Digital sum moments and substitutions
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
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 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
Diophantine approximation, Hausdorff dimension and Schroder's functional equation
Diophantine Approximation in certain Solenoids
Diophantine Approximations of Infinite Series and Products
This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos' results on~irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.
Diophantine classes, dimension and Denjoy maps
Discrete self-similar multifractals with examples from algebraic number theory
Distance sets, ratio sets and certain transformations of sets of real numbers
Distribution measures and Hausdorff dimensions.
Dyadische Entwicklungen und Hausdorffsches Mass
Dynamical directions in numeration
This survey aims at giving a consistent presentation of numeration from a dynamical viewpoint: we focus on numeration systems, their associated compactification, and dynamical systems that can be naturally defined on them. The exposition is unified by the fibred numeration system concept. Many examples are discussed. Various numerations on rational integers, real or complex numbers are presented with special attention paid to -numeration and its generalisations, abstract numeration systems and...
Dynamiques associees a une echelle de numeration