Featured Speakers:
8am - 9am: Raphaël Krikorian (Ecole Polytechnique)
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.
9am - 10am: Bertrand Deroin (CNRS - CYU)
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.
10am - 11am: Giovanni Forni (CYU - University of Maryland)
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.
Organizers:
Zhiqiang Li (Peking University)
Misha Lyubich(Stony Brook University)
Michael Yampolsky(University of Toronto)
