Zhiqiang Li
(Peking University, China)
Misha Lyubich
(Stony Brook University, USA)
Michael
Yampolsky (University of Toronto, Canada)
Speaker 1 Sylvain Crovisier (Université
Paris-Saclay, France)
Title: A Closing Lemma for Hénon maps of R2.
Abstract: I will discuss some dynamical properties
of mildly dissipative diffeomorphisms of the plane, which includes Hénon maps
with jacobian smaller than 1/4. Some years ago we proved with Enrique Pujals a
closing lemma: the support of any invariant measure is contained in the closure
of the set of periodic points. I will present a stronger version of this
closing lemma and state some consequences. In particular any ergodic measure is
supported on a periodic orbit, on an homoclinic class or on an odometer.
(Collaboration with E. Pujals)
Speaker 2 Andrey Mironov (Novosibisrk State
University, Russia)
Title: Integrable billiards inside cones.
Abstract: We study Birkhoff billiards inside cones
in $\mathbb{R}^n$. We show that every trajectory inside a cone over a $C^3$
strictly convex closed hypersurface embedded in $\mathbb{R}^{n-1}$ with
non-degenerate second fundamental form undergoes only finitely many
reflections. Using this result, we prove that the system is both
superintegrable and completely integrable. To our knowledge, this provides the
first example of an integrable billiard in which the billiard table is neither
a quadric nor composed of pieces of quadrics. The results are
obtained with Siyao Yin.
Speaker 3 Selim Ghazouani (University College
London, UK)
Title: A conjecture about parabolic dynamical systems
Abstract: A parabolic dynamical system is,
loosely, a smooth diffeomorphism whose orbits exhibit slow (polynomial)
sensitivity to initial conditions. In this talk, I will make the case for the
following conjecture: unlike the handful of examples that are well-understood,
the generic parabolic dynamical system satisfies the central limit theorem.
This case will be based upon numerical experiments and heuristic considerations.
Speaker 4 Amie Wilkinson (University of Chicago, US)
Title: TBC
Abstract: TBC
Zoom
Meeting ID: 827 8743 3327
Passcode:
692502
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: 5/27/2026