Sequences and dynamical systems associated with canonical approximation by rationals
S-expansions in dimension two
The technique of singularization was developped by C. Kraaikamp during the nineties, in connection with his work on dynamical systems related to continued fraction algorithms and their diophantine approximation properties. We generalize this technique from one into two dimensions. We apply the method to the the two dimensional Brun’s algorithm. We discuss, how this technique, and related ones, can be used to transfer certain metrical and diophantine properties from one algorithm to the others. In...
Some applications of Elliot's mean-value theorem.
Some asymptotic results associated with a generalized Gauss-Kuzmin-type operator.
Some remarks on Diophantine approximation by the Jacobi-Perron algorithm
Some special W-almost periodic sets on the integers.
Spectral properties of arithmetic functions
Spectre de certaines fonctions presque périodiques (au sens de Bohr)
Statistical convergence of subsequences of a given sequence.
Statistical convergence of subsequences of a given sequence
This paper is closely related to the paper of Harry I. Miller: Measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc. 347 (1995), 1811–1819 and contains a general investigation of statistical convergence of subsequences of an arbitrary sequence from the point of view of Lebesgue measure, Hausdorff dimensions and Baire’s categories.
Strong convergence of additive Multidimensional Continued Fraction algorithms
Suites à spectre vide et suites pseudo-aléatoires
Suites uniformément distribuées et fonctions faiblement presque-périodiques
Sur Certaines Suites Pseudo-Aléatoires III.
Sur la mesure spectrale de certaines suites arithmétiques
Sur la mesure spectrale des suites multiplicatives
Dans cet article, nous démontrons que la mesure spectrale d’une suite multiplicative de module dont le spectre de Fourier-Bohr est non vide, est atomique. La preuve, basée sur un résultat de J.-P. Bertrandias, évite le calcul de la corrélation.
Sur l'équirépartition des suites à croissance lente et des suites non décroissantes
Systems of linear forms and covers for star bodies