Jean-Pierre Conze

Sur un critère de récurrence en dimension 2 pour les marches stationnaires, applications

The present disclosure relates to a rotatable member assembly such as a pulley wheel, a sheave or drive pulley or the like fabricated from a pair of metal disks stamped from sheet metal stock and welded together in a novel manner. The disk members are each provided with an outer peripheral rim, a web portion having an annular laterally extending weld projection formed thereon, and a central hub-engaging section. To assemble the member, a bearing, bushing, or hub is positioned in the central hub-engaging section and the disks are placed together and subjected to heat and pressure at the web portion so that the weld projection of one of the disks fuses with the weld projection of the other disk to form an integral assembly.

Limit law for some modified ergodic sums

An example due to Erdos and Fortet shows that, for a lacunary sequence of integers (q_n) and a trigonometric polynomial f, the asymptotic distribution of normalized sums of f(q_k x) can be a mixture of gaussian laws. Here we give a generalization of their example interpreted as the limiting behavior of some modified ergodic sums in the framework of dynamical systems.

Dynamics of Some Contracting Linear Functions Modulo 1

In various problems in signal theory, the following family of functions of [0, 1]into itself arises naturally :

Almost everywhere convergence of convolution powers on compact Abelian groups

T_{\gamma ,\alpha } :x \mapsto \gamma x + \alpha modulo 1, with 0 < \gamma < 1,0 \leqslant \alpha < 1.

Almost periodic measures on the torus

The purpose of the present work is to describe very precisely the asymptotic behaviour of the iterates of the functions Tγ,α. Further, we give a continued fraction type algorithm which allows us to obtain, for a given pair (γ,α), the numerical information on the dynamic of Tγ,α.

Théorèmes ergodiques pour des mesures diagonales

Nous considerons un sous-groupe Γ du groupe lineaire G = Sl(d, ℝ), le sous-groupe N des matrices unipotentes triangulaires superieures et le sous-groupe A des matrices diagonales positives. Le sous-groupe Γ est suppose discret et ≪ non elementaire ≫. En utilisant plusieurs notions de points limites pour Γ, nous etudions la densite des orbites de Γ dans certains fermes Γ-invariants canoniques de ℝ d , et de ses produits exterieurs. Nous considerons aussi, par dualite, l’action de N sur Γ\G, puis l’action de A sur Γ\G. Nous utilisons une methode basee sur les proprietes d’equidistribution de marches aleatoires sur ℝ d ou G/N.

Fonctions harmoniques pour un opérateur de transition et applications

It is well-known that a probability measure μ on the circle T satisfies ‖μn ∗ f − ∫ f dm‖p → 0 for every f ∈ Lp , every (some) p ∈ [1,∞), if and only if |μ̂(n)| < 1 for every non-zero n ∈ Z (μ is strictly aperiodic). In this paper we study the a.e. convergence of μn ∗ f for every f ∈ Lp whenever p > 1. We prove a necessary and sufficient condition, in terms of the Fourier– Stieltjes coefficients of μ, for the strong sweeping out property (existence of a Borel set B with lim supμn ∗ 1B = 1 a.e. and lim infμn ∗ 1B = 0 a.e.). The results are extended to general compact Abelian groups G with Haar measure m, and as a corollary we obtain the dichotomy: for μ strictly aperiodic, either μn ∗ f → ∫ f dm a.e. for every p > 1 and every f ∈ Lp(G,m), or μ has the strong sweeping out property. Résumé. Il est connu qu’une mesure de probabilité μ sur le cercle T satisfait ‖μn ∗ f − ∫ f dm‖p → 0 pour toute fonction f ∈ Lp et pour tout p ∈ [1,∞) (ou pour un p ∈ [1,∞)), si et seulement si μ est strictement apériodique (i.e. |μ̂(n)| < 1 pour tout n non nul dans Z). Nous étudions ici la convergence presque partout de μn ∗ f pour f ∈ Lp , p > 1. Nous montrons une condition nécessaire et suffisante portant sur les coefficients de Fourier–Stieltjes de μ pour la propriété de “balayage fort” (existence d’un borélien B tel que lim supμn ∗ 1B = 1 p.p. et lim infμn ∗ 1B = 0 p.p.). Les résultats sont étendus aux groupes abéliens compacts généraux G de mesure de Haar m. Comme corollaire nous obtenons la dichotomie suivante : pour μ strictement apériodique, soit μn ∗ f → ∫ f dm p.p. pour tout p > 1 et toute fonction f ∈ Lp(G,m), soit μ vérifie la propriété de balayage fort. MSC: Primary 37A30; 28D05; secondary 47A35; 60G50; 42A38

Régularité des bases d'ondelettes et mesures ergodiques.

The liftable centralizer for special flows over irrational rotations is studied. It is shown that there are such flows under piecewise constant roof functions which are rigid and whose liftable centralizer is trivial.