## IHP

Institut Henri Poincaré

## COUSINS Benjamin

Date:
Lun, 19/01/2015 - Ven, 23/01/2015
Site:
Nom:
COUSINS
Prénom:
Benjamin
Origine:
Université d'Atlanta
Origine:
États-Unis
Thème:
WINTER SCHOOL 2015
Invitant:
FRADELIZI Matthieu
Invitant:
GOZLAN Nathaël
Invitant:
SAMSON Paul-Marie

## BRAZITIKOS Silouanos

Date:
Lun, 19/01/2015 - Ven, 23/01/2015
Site:
Nom:
BRAZITIKOS
Prénom:
Silouanos
Origine:
Grèce
Thème:
WINTER SCHOOL 2015
Invitant:
FRADELIZI Matthieu
Invitant:
GOZLAN Nathaël
Invitant:
SAMSON Paul-Marie

## Continuity of core entropy of quadratic polynomials

Type:
Type:
Site:
Date:
19/12/2014 - 10:30
Salle:
01
Orateur:
TIOZZO Giulio
Localisation:
Université Yale
Localisation:
États-Unis
Résumé:

The core entropy of polynomials, recently introduced by W. Thurston, is a dynamical invariant which can be defined purely in combinatorial terms, and provides a useful tool to study parameter spaces of polynomials. The theory of core entropy extends to complex polynomials the entropy theory for real unimodal maps: the real segment is replaced by an invariant tree, known as Hubbard tree, which lives inside the filled Julia set. We prove that the core entropy of quadratic polynomials varies continuously as a function of the external angle, answering a question of Thurston.

## Exposants de Lyapunov en dynamique uni-dimensionnelle

Type:
Type:
Site:
Date:
12/12/2014 - 14:00
Salle:
Amphi Darboux
Orateur:
Neil Dobbs
Localisation:
Université de Genève
Localisation:
Suisse
Résumé:

En dynamique réelle uni-dimensionnelle, il existe un fort lien entre les exposants de Lyapunov des points typiques (par rapport à la mesure de Lebesgue) et l'existence de mesure de probabilité invariante et absolument continue par rapport à la mesure de Lebesgue. Ce lien persiste, on espère, en dynamique rationnelle. Pour les applications de type Misiurewicz de la famille exponentielle $z \mapsto \lambda e^z$, les exposants de Lyapunov pour des points typiques n'existent même pas.

## Caractérisation de revêtements ramifiés par des graphes finis

Type:
Type:
Site:
Date:
28/11/2014 - 10:30
Salle:
421
Orateur:
Bastien Rossetti
Localisation:
Université Toulouse 3
Localisation:
France
Résumé:

On va décrire, pour un revêtement ramifié (par la sphère au-dessus de la sphère) postcritiquement fini $f$ à orbifold hyperbolique, un graphe fini qui, s'il existe, caractérise $f$. Cela signifie que si un deuxième revêtement ramifié $g$ possède le "même" graphe alors $f$ et $g$ sont Thurston équivalents. Si $f$ et $g$ sont des fractions rationnelles cela conduit à une conjugaison par une transformation de Möbius. On va construire de tels graphes pour certains accouplements et on verra un exemple d'utilisation.

## Univalent maps as pseudo-conjugacies between rational map perturbations

Type:
Type:
Site:
Date:
24/10/2014 - 10:30
Salle:
05
Orateur:
Tan Lei
Localisation:
Université d'Angers
Localisation:
France
Résumé:

We will see in examples how univalent maps arise as pseudo-conjugacies in a dynamical perturbation of a rational map, how to control their conformal and spherical distortions and how to use these controls to get ray-landing properties in the parameter space of rational maps.

## Julia sets, snowflakes and distortion of dimension under a holomorphic motion of a circle

Type:
Type:
Site:
Date:
10/10/2014 - 10:30
Salle:
421
Orateur:
Kari Astala
Localisation:
Université d'Helsinki
Localisation:
Finlande
Résumé:

Holomorphic motions provide a bridge between analysis and complex dynamics, and provide also powerful tools for the quasiconformal mappings. Basic examples of holomorphic motions are given by Julia sets when parameters of polynomials are varied, and these give important examples within different topics in analysis, as well.

In this talk, based on a joint work with Ivrii, Prause and Perälä, we are interested in maximal growth of dimension under holomorphic motions of Julia sets. In particular, consider the family $P(z) = z^d + tz$ with $|t| <1$. Slodkowski's theorem allows for the Böttcher coordinates a natural extension to a holomorphic motion of the plane. But can there exist a better one ?

## Fast basins, fractal manifolds, and flows on attractors of iterated function systems (IFSs)

Type:
Type:
Site:
Date:
06/06/2014 - 10:30
Salle:
421
Orateur:
Michael Barnsley
Localisation:
Université nationale australienne
Localisation:
Australie
Résumé:

Since their introduction, thirty years ago, IFSs have become a widely used concept. Reasons for this success include the simplicity of the IFSs themselves and the richness of their attractors. This talk will define, characterize, and exemplify, a number of new basic structures that arise naturally from an attractor of an IFS. The driving force behind these structures is a direct generalization of the notion of analytic continuation from smooth to rough.

## On the Hausdorff Dimension of the quadratic Julia sets near to the parabolic points

Type:
Type:
Site:
Date:
16/05/2014 - 10:30
Salle:
314
Orateur:
Ludwik Jaksztas
Localisation:
Université de Varsovie
Localisation:
Pologne
Résumé:

Let d(c) denote the Hausdorff dimension of the Julia set of the polynomial z^2+c. I will discuss the behaviour (derivative) of the function d(c) where the real parameter c is close to the parabolic points, especially 1/4 (parabolic point with one petal) and -3/4 (point with two petals).

## On McMullen-like mappings

Type:
Type:
Site:
Date:
04/04/2014 - 10:30
Salle:
421
Orateur:
Sébastien Godillon
Résumé:

McMullen has proved that the Julia set of $z^n+\lambda/z^d$ is a Cantor of Jordan curves as soon as the local degrees $n$ and $d$ satisfy a certain arithmetic condition (and $|\lambda|>0$ is small enough). Many other authors have studied similar examples obtained by adding singular perturbations to a polynomial. I will introduce a general definition of the so called McMullen-like mappings that unifies this behavior. Every topological conjugation class is described by the data of a postcritically finite hyperbolic polynomial and a collection of local degrees, each associated with a periodic Fatou domain. Using this invariant, the arithmetic condition for existence can be generalized. I will show that this condition is actually necessary by using the theory of Thurston's obstructions.