Journée Amiénoise de Systèmes Dynamiques 2016

Le 26 avril 2016 au LAMFA
UPJV - Salle BC 101

Programme de la Journée

9h: Accueil des participants

9h30-10h30: Yûzuke Okuyama (Kyoto Institute of Technology)
A Mahler-type estimate of weighted Fekete sums
on the Berkovich projective line

We will talk about a Mahler-type estimate of weighted Fekete sums on the Berkovich projective line, which is asymptotically sharp.

10h45-11h45: Marie Albenque (CNRS - Ecole Polytechnique)
Convergence de cartes planaires aléatoires

In the last years, numerous families of planar maps (embeddings of planar graphs in the sphere) have been shown to converge to the Brownian map introduced by Miermont and Le Gall. I’ll describe in this talk this result of Miermont and Le Gall together with its context and will prove a similar result for simple triangulations.

This work relies first on a bijection between simple triangulations and a certain class of decorated trees. Then the distance in the maps can be studied with the help of some canonical « leftmost paths », which behave well both in the map and in the tree. I’ll emphasize the combinatorial constructions that play a major role in this work and which gives a glimpse of into the structure of the Brownian map.

11h45-13h45: Déjeuner

13h45-14h45: Frédéric Bayart (Université Blaise Pascal)
Central limit theorems in linear dynamics
Given a bounded operator T on a Banach space X, we study the existence of a probability measure µ on X such that, for many functions f : X--->K, the sequence (f + ... + f o T^{n-1})/n^{1/2} converges in distribution to a Gaussian random variable.

15h-16h: Mariusz Lemanczyk (Nicolaus Copernicus University)
Approximate orthogonality of powers for Rokhlin extensions of rotations

An automorphism T is called to have  asymptotically orthogonal powers (AOP), if its different prime powers T^p and T^q become closer and closer to be disjoint in the sense of Furstenberg when p,q tend to infty. Quasi-discrete spectrum automorphisms are known to enjoy the AOP property. I will show how this property can be achieved in the class of so-called Rokhlin extensions of irrational rotations. This will allow us to produce ergodic sequences (a_n) of integers along which, for any uniquely ergodic homemorphism S, we have all observables f(S^{a_n}x), (n in N), orthogonal to any multiplicative arithmetic function u from N to C, with |u| at most 1. The talk is based on my joint work with Joanna Kulaga-Przymus.

La Cathédrale d'Amiens

Comment venir au LAMFA: lien

Laboratoire Amiénois de mathématiques