Définition de paramètres d'équirépartition
Der Satz von Hurwitz beim Jacobialgorithmus.
Développement en fraction continue à l'entier supérieur, idéaux 0-réduits et un problème d'Eisenstein
Diophantine approximation in short intervals
Diophantine approximation on Veech surfaces
We show that Y. Cheung’s general -continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an appropriate sense. The saddle connection continued fractions then allow one to recognize certain transcendental...
Diophantine approximation with partial sums of power series
We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.
Diophantische Approximationen von: Irrationalzahlen mit Kettenbruchnennern von eingeschränktem Wachstum
Discrete planes, -actions, Jacobi-Perron algorithm and substitutions
We introduce two-dimensional substitutions generating two-dimensional sequences related to discrete approximations of irrational planes. These two-dimensional substitutions are produced by the classical Jacobi-Perron continued fraction algorithm, by the way of induction of a -action by rotations on the circle. This gives a new geometric interpretation of the Jacobi-Perron algorithm, as a map operating on the parameter space of -actions by rotations.
Distances dans la suite des multiples d'un point du tore à deux dimensions
Introduction. Soit θ un élément de ¹=ℝ/ℤ. Considérons la suite des multiples de θ, . Pour tout n ∈ ℕ, ordonnons les n+1 premiers termes de cette suite, 0 = y₀ ≤ y₁ ≤...≤ yₙ ≤ 1 = pθ, p=0,...,n. La suite (y₀,...,yₙ) découpe l’intervalle [0,1] en n+1 intervalles qui ont au plus trois longueurs distinctes, la plus grande de ces longueurs étant la somme des deux autres. Cette propriété a été conjecturé par Steinhaus, elle est étroitement liée au développement en fraction continue de θ. On peut aussi...
Distribution of closed geodesics on the modular surface and quadratic irrationals
Distribution of Lévy constants for quadratic numbers
Dyadic Fractions with Small Partial Quotients.
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...
Dynamics of a continued fraction of Ramanujan with random coefficients.
Dynamics of the continued fraction map and the spectral theory of SL (2, Z).