Absorbing sets of homogeneous subtractive algorithms

We consider homogeneous multidimensional continued fraction algorithms, in particular a family of maps which was introduced by F. Schweiger. We prove his conjecture regarding the existence of an absorbing set for those maps. We also establish that their renormalisations are nonergodic which disproves another conjecture due to Schweiger. Other homogeneous algorithms are also analysed including ones which are ergodic

Discretisations des homeomorphismes du cercle

a paraitre dans Ergodic Theory and Dynamical SystemsOn s'interesse aux proprietes asymptotiques de la suite des discretisations uniformes d'un homeomorphisme du cercle. On etudie leurs dependances en les proprietes arithmetiques du nombre de rotation de l'homeomorphisme en question. En particulier, on considere la structure des cycles periodiques, leurs distributions spatiales et le temps de stabilisation du processus de discretisation

Central limit theorem for a Gaussian incompressible flow with additional Brownian noise

We generalize the result of T. Komorowski and G. Papanicolaou. We consider the solution of stochastic differential equation $dX(t)=V(t,X(t))dt+\sqrt{2\kappa}dB(t)$ where $B(t)$ is a standard $d$-dimensional Brownian motion and $V(t,x)$, $(t,x)\in R \times R^{d}$ is a $d$-dimensional, incompressible, stationary, random Gaussian field decorrelating in finite time. We prove that the weak limit as \ep\downarrow 0 of the family of rescaled processes $X_{\epsilon}(t)=\epsilon X(\frac{t}{\epsilon^{2}})$ exists and may be identified as a certain Brownian motion

Formes normales d'une metrique mixte analytique reelle generique

Par une metrique mixte on comprend une metrique definie dans un domaine du plan, changeant de caractere - sur une region elle est riemannienne, sur une autre lorentzienne. On se place dans un point appartenant a la frontiere entre ces deux regions et on cherche une forme locale ``la plus simple" de notre metrique - un probleme analogue a l'existance des coordonnees isothermes dans le cas classique, riemannien ou lorentzien. On montre que generiquement on peut se ramener a un seul modele conforme $du^{2}+vdv^{2}$. Il existe tout de meme des points specifiques ou l'espace des modeles conformes est de dimension infinie

Cartan connection of transversally Finsler foliation

The purpose of this paper is to define transversal Cartan connectionof Finsler foliation and to prove its existence and uniqueness

Projective spaces of second order

Grassmannians of higher order appeared for the first time in a paper of A. Szybiak ([3]) in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian—the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group