Background
The workshop will be preceded by introductory mini-courses (May 5-9, 2008), suitable for advanced graduate students or interested postdoctoral mathematicians. One of the mini-courses will consist of the Aisenstadt lectures by Jean-Christophe Yoccoz (Collège de France). In addition there will be mini-courses by Richard Montgomery (UC Santa Cruz) and Laurent Stolovitch (Université Paul Sabatier).
Mini-Courses Program
The purpose of the workshop is to bring together people having different expertises around the general theme of dynamical systems and their singularities, and the role they play in ODE and PDE. Among the participants there will be specialists of geometrical methods in differential equations, geometric analysis, the analysis of Hamiltonian systems and Hamiltonian PDE, summability techniques in complex dynamics, small divisor problems and KAM theory, and applications of dynamical systems to PDE. The subjects covered include:
(1) Normal forms for singularities of dynamical systems (ODE and difference equations). This will include the study of normal forms of families depending on parameters and the new light this sheds on the divergence of the normalizing transformations. This will also include the recent studies of divergence of Birkhoff normal forms for integrable, however non-analytic, Hamiltonian vector fields and applications to bifurcation problems.
(2) Singularities in Poisson structures, as in the work of Marsden & Weinstein and the recent studies by L. Stolovich.
(3) Resonances, such as in the classical results of Duistermaat and the more recent work of Bourgain.
(4) Recent progress in KAM theory, including its extensions to partial differential equations and the study of resonant tori.
(5) Variational problems in dynamical systems, including the recently discovered figure eight and hip-hop choreographies for the n-body problem, Morse-Hedlund theory of connecting geodesics, and Mather theory for the variational approach to Arnold diffusion.