Séminaire Géométrie, analyse et dynamique

Séminaire Géométrie, analyse et dynamique


Laboratoire Dieudonné-CNRS-UNS UMR 7351

Le Séminaire a lieu le Mardi à 14h00 en salle I du LJAD

Accès au laboratoire J.A. Dieudonné

Prochain exposé

Mardi 6 Novembre            
     Indira Chatterji


Au programme


Mardi 13 Novembre            
     Peter Smillie (IHES)

Mardi 20 Novembre            
     Gérard Iooss (LJAD)
Existence de quasipatterns dans la superposition de deux patterns hexagonaux

Let us consider a quasilattice, spanned by the superposition of two hexagonal lattices in the plane, differing by a rotation of angle ß. We study bifurcating quasipatterns solutions of the Swift-Hohenberg PDE, built on such a quasilattice, invariant under rotations of angle π /3. For nearly all ß, we prove that in addition to the classical hexagonal patterns, there exist two branches of bifurcating quasipatterns, with equal amplitudes on each basic lattice.

Mardi 27 Novembre            
     Bram Petri (Uni Bonn)


Mardi 26 Mars            
     Rémi Coulon

Exposés passés


Mardi 11 Septembre      Jayadev Athreya
Random Tesselations of Hyperbolic Surfaces

In joint work with Lalley, Sapir, and Wroten, we study the statistics of the tesselations of hyperbolic surfaces induced by long random geodesics. We show that the local statistics approach that of a Poisson Line Process. All relevant notions will be defined.

Mardi 25 Septembre      Xiang Zhang (Shanghai Jiao Tong University -- China)
Global and local integrability of differential systems and its application

In this talk we report the progress on the study of both global integrability and local integrability of ordinary differential systems, and also their applications. On global integrability we emphasis on algebraic aspects, especially Darboux theory of integrability and its relation with Liouvillian integrability. On local integrability, we concern the necessary and sufficient conditons of ordinary differential system in a neighborhood of a singular point, which has also connection with global integrability.


Mardi 2 Octobre      Qun Wang (CEREMADE, Université Paris-Dauphine)
Periodic Solution for Positive N-vortex Problem: Existence, Multiplicity and Symmetry.

The vortex dynamics finds its root in hydrodynamics with 160 years of history. In 1858 Hermann von Helmholtz’s seminal paper has marked its birth and then Kirchhoff in 1876 has shown its Hamiltonian structure. It is well known that for N>3 this problem is in general non-integrable, thus the searching of periodic solution serves as an important approach to understand the dynamics. Many interesting results in this fields are produced through methods developed in celestial mechanics, especially perturbative aspects. On the other hand, in recent years following the figure eight solution of Chenciner and Montgomery, variational methods have been proved to be very efficient in searching for periodic solutions in N-body problem. In this talk I would like to explore the possibility in application of classical variational methods in Hamiltonian system to the study of periodic solutions for N-vortex systems with positive vorticities in the plane, including their existence, multiplicity, and possible symmetry.

Mardi 9 Octobre      Alain Chenciner (ASD & Paris 7)
Les coordonnées actions-angles - Une simple histoire d’action de tore (d’après Nguyen Tien Zung)

On sait bien que l’existence de coordonnées actions-angles est intimement liée à l’action de tore associée à un système intégrable. Nguyen Tien Zung renverse le point de vue en montrant que tout tenseur préservé par le système l’est aussi par cette action. D’où tout s’ensuit.

Mardi 16 Octobre      Mauricio Poletti (Université Paris-Sud)
Positive exponents for random product of diffeomorphisms

We prove that in the space of C^r random product of volume preserving diffeomorphisms there exists a C^1 dense and C^1 open set with positive Lyapunov exponents. We actually prove this in the more general setting of skew products with a hyperbolic homeomorphism as a base map and for volume preserving skew products. This is a joint work with Davi Obata.

Archives du séminaire de géométrie, analyse et dynamique: 2016/2017, 2017/2018
Archives du séminaire de géométrie et analyse: 2007/2008, 2008/2009, 2009/2010, 2010/2011, 2011/2012, 2012/2013, 2013/2014, 2014/2015, 2015/2016
Archives du séminaire de géométrie et dynamique: ici

Organisation: Zhiyan Zhao (écrire) et Emmanuel Militon (écrire)