## IHP

Institut Henri Poincaré

## Groupe de travail Courbure, Transport Optimal, et Probabilités (CTOP)

Site:
IHP
Organisateur(s):
FRADELIZI Matthieu

Ce groupe de travail est dédié à l'étude des liens entre Courbure, Transport Optimal, et Probabilités (C-TOP !). Il a lieu à l'Institut Henri Poincaré (IHP) et fait partie des événements de l'ANR GeMeCoD. Page du groupe de travail.

Date Orateur Site Titre
15/06/2017 - 14:00 ZVAVITCH Artem
Université d'État de Kent
États-Unis
IHP
01
On the convexification effect of Minkowski summation

## On the convexification effect of Minkowski summation

Type:
Site:
Date:
15/06/2017 - 14:00
Salle:
01
Orateur:
ZVAVITCH Artem
Localisation:
Université d'État de Kent
Localisation:
États-Unis

## Large deviation for return times

Type:
Type:
Site:
Date:
02/02/2018 - 10:30
Salle:
421
Orateur:
COUTINHO Adriana
Localisation:
Université de Bahia
Localisation:
Brésil
Résumé:

We prove a large deviation result for return times of the orbits of a dynamical system in a r-neighbourhood of an initial point x. Our result may be seen as a dierentiable version of the work by Jain and Bansal who considered the return time of a stationary and ergodic process defined in a space of infinite sequences.

## Genericity of weak mixing in negative curvature

Type:
Type:
Site:
Date:
08/12/2017 - 15:15
Salle:
05
Orateur:
BELARIF Kamel
Résumé:

Let $M$ be a manifold with pinched negative sectional curvature. We show that, when $M$ is geometrically finite and the geodesic flow on $T^1M$ is topologically mixing, the set of mixing invariant measures is dense in the set $P(T^1M)$ of invariant probability measures. This implies that the set of weak-mixing measures which are invariant by the geodesic flow is a dense $G_\delta$ subset of $P(T^1M)$. We also show how to extend these results to geometrically infinite manifolds with cusps or with constant negative curvature.

## The rigidity conjecture

Type:
Type:
Site:
Date:
08/12/2017 - 14:00
Salle:
05
Orateur:
PALMISANO Liviana
Localisation:
Université de Bristol
Localisation:
Royaume-Uni
Résumé:

A central question in dynamics is whether the topology of a system determines its geometry, whether the system is rigid. Under mild topological conditions rigidity holds in many classical cases, including: Kleinian groups, circle diffeomorphisms, unimodal interval maps, critical circle maps, and circle maps with a break point. More recent developments show that under similar topological conditions, rigidity does not hold for slightly more general systems. We will discuss the case of circle maps with a flat interval. The class of maps with Fibonacci rotation numbers is a $C^1$ manifold which is foliated with co dimension three rigidity classes. Finally, we summarize the known non-rigidity phenomena in a conjecture which describes how topological classes are organized into rigidity classes.

## On the abundance of SRB measures

Type:
Type:
Site:
Date:
10/11/2017 - 15:15
Salle:
05
Orateur:
YANG Dawei
Localisation:
Université de Suzhou
Localisation:
République populaire de Chine
Résumé:

We prove the existence of Sinai-Ruelle-Bowen measures for a class of $C^2$ partially hyperbolic diffeomorphisms via the method of random perturbations. This is a joint work with Y. Cao and Z. Mi.

## Hausdorff dimensions and hitting probabilities of random covering sets

Type:
Type:
Site:
Date:
10/11/2017 - 14:00
Salle:
05
Orateur:
LI Bing
Localisation:
Université de technologie de Chine méridionale
Localisation:
République populaire de Chine
Résumé:

The Dvoretzky random covering problem is to find the conditions for which almost surely every point on the circle is covered infinitely many times by a sequence of random intervals with decreasing lengths and random initial points (an i.i.d. sequence of random variables uniformly distributed on the circle). It has drawn a lot of interest of many mathematicians for the last decades and the sizes of the random covering sets have been widely studied. The Hausdorff dimensions and hitting probabilities of random covering sets will be given in the talk. The covering setting also was generalized to many different cases, for example, covering the torus with rectangles or open sets, or even just Lebesgue measure sets, or balls with singular distributions, some recent related results will be surveyed.

## TANGUY Kévin

Date:
Jeu, 27/04/2017
Site:
Nom:
TANGUY
Prénom:
Kévin
Origine:
INP Toulouse
Origine:
France
Thème:
Collaboration scientifique
Invitant:
FRADELIZI Matthieu

## Mélangeurs en dynamique complexe

Type:
Type:
Site:
Date:
17/03/2017 - 10:30
Salle:
05
Orateur:
Johan Taflin
Localisation:
Université de Dijon
Localisation:
France
Résumé:

Récemment Dujardin a introduit en dynamique complexe la notion de mélangeurs originalement due à Bonatti et Díaz. Dans cet exposé, j'expliquerai que de tels objets apparaissent toujours proche d'une bifurcation d'une application produit en dimension 2 et qu'il en existe en fait de deux types : répulsifs et selles. Les premiers donnent lieu à des ouverts de bifurcations alors que les seconds permettent d'obtenir des attracteurs d'intérieur non vide.

## BIGOT Jérémie

Date:
Jeu, 23/02/2017
Site:
Nom:
BIGOT
Prénom:
Jérémie
Origine:
Université Bordeaux 1
Origine:
France
Thème:
Séminaire Ctop
Invitant:
FRADELIZI Matthieu