October 3 – 7, 2016
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The study of dynamical systems on surfaces goes back to Poincaré and Birkhoff, with motivations from celestial mechanics. Here are three examples of recent lines of research:
(1) The rotation set was introduced in the 80’s; numerous results were obtained recently that reveal the links between the rotation set and the dynamical structure; (2) The realisation of the Zimmer conjecture on surfaces, by Polterovich and Franks-Handel, has drawn attention of researchers on group actions on surfaces; (3) The Arnol’d conjecture, which generalizes the famous Poincaré-Birkhoff theorem, has motivated the development of Floer homology in symplectic geometry; on surfaces, this leads to a fruitful dialogue between the symplectic and topological concepts. The developement of topological tools also allows to describe the dynamics from a global viewpoint, and are also fruitful for studying differentiable systems Dynamics on surfaces are represented in South America, the United States, Japan, France, Germany, … This conference will give the opportunity to share the latest advances and the new methods of the subject. It is a natural sequel to Surfaces in Montevideo (2012) and Surfaces in Sao Paulo (2014). |
Scientific Committee
John Franks (Northwestern University) Organizing Committee François Béguin (Institut Galilée, Paris 13) |
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Mini-courses
The ergodic theory of groups of diffeomorphisms of the circle Abstract: We will review some recent advances and open problems, on the dynamical theory of groups of diffeomorphisms of the circle. We will more precisely study the relation between the ergodic and topological properties of the action.
Forcing theory for transverse trajectories of surface homeomorphisms Abstract: Several recent papers on surface dynamics have used transverse foliations and maximal isotopies for homeomorphisms isotopic to the identity as a main tool in their work. In this mini-course we will introduce the basic concepts behind this tool and show a new way o deriving useful dynamical information by means of a forcing procedure. The applications involve ways of obtaining existence of non-contractible periodic points with consequences for rotation sets of toral homeomorphisms, exponential growth of periodic orbits and estimates on topological entropy of maps. |
Talks
Global dynamics for symmetric planar maps
The almost-Borel structure of surface diffeomorphisms
Super generalized pseudo-Anosov maps
Shub conjecture for smooth self-maps of the sphere
Generic homeomorphisms and rotation sets
On the dynamics of minimal homeomorphisms of T2
A Poincaré Bendixson theorem for translation lines and applications to invariant continua
Orderability and groups of homeomorphisms of the circle
Nontrivial attractor-repellor maps of S2 and rotation numbers
Franks-Misiurewicz conjecture for extensions of irrational rotations
Some dynamical applications of Carathéodory’s prime ends theory
C0 Hamiltonian dynamics and the Arnold conjecture
The Ogasa invariant for homology spheres in dimension 3 |