Zhiqiang Li
(Peking University, China)
Misha Lyubich
(Stony Brook University, USA)
Michael Yampolsky
(University of Toronto, Canada)
Speaker 1 Raphaël Krikorian (Institut Polytechnique
De Paris, France):
Title: Exotic rotation domains and Herman rings for
quadratic Hénon maps
Abstract: Quadratic Hénon
maps are polynomial automorphism of $\mathbb{C}^2$ of
the form $h:(x,y)\mapsto (\lambda^{1/2}(x^2+c)-\lambda y,x)$.
They have constant Jacobian equal to $\lambda$ and they admit two fixed points.
If $\lambda$ is on the unit circle (one says the map $h$ is conservative) these
fixed points can be elliptic or hyperbolic. In the elliptic case, a simple
application of Siegel Theorem shows (under a Diophantine assumption) that $h$
admits many quasi-periodic orbits with two frequencies in the neighborhood of
its fixed points. Surprisingly, in some hyperbolic cases, S. Ushiki observed some years ago what seems to be
quasi-periodic orbits though no Siegel disks exist. I will explain why this is
the case. This theoretical framework also predicts and mathematically proves,
in the dissipative case ($\lambda$ of module less than 1), the existence of
(attractive) Herman rings. These Herman rings, which were not observed before,
can be produced in numerical experiments.
Speaker 2 Bertrand Deroin (CNRS - CYU, France):
Title: Towards a Structural Stability Theory for
Holomorphic Foliations on Algebraic Complex Surfaces
Abstract: I'll review work done in collaboration
with Aurélien Alvarez, aiming at developing a theory
of structural stability for holomorphic foliations on compact complex surfaces.
Important new examples are the Jouanolou foliations
of the complex projective plane, and the fundamental properties they satisfy
allow us to define a more general family of foliations on arbitrary algebraic
surfaces, which we call Jouanolou-type foliations. I
will present these conditions, as well as some of their properties, and, time
permitting, I will state a number of conjectures.
Speaker 3 Giovanni Forni (CYU, France - University of
Maryland, USA)
Title: On the dynamics of billiards in polygons
Abstract: In this talk we will survey several
results on the dynamics of billiards in polygons. These include
results on their ergodic theory (weak mixing), KAM-type results on stability of
invariant surfaces of rational billiards under perturbations and existence of
periodic orbits. Part of the work is in collaboration with F. Arana Herrera and
J. Chaika.
Last Updated: 10/25/2025