Report 31/2005: Dynamical Systems (July 10th -- July 16th, 2005) (Q870673)

Summary: This workshop continues the biannual series at Oberwolfach on Dynamical Systems that started as the ``Moser-Zehnder meeting'' in 1981. The main theme of the workshop are the new results and developments in the area of classical dynamical systems, in particular, in celestial mechanics and Hamiltonian systems. Among the main topics are new global results on the Reeb dynamics on 3-manifolds, KAM theory in finite and infinite dimensions, as well as new developments in Floer homology and its applications. High points are the first complete existence proof of quasiperiodic solutions in the planetarian \(N\)-body problem, and the solution of a long-standing conjecture of Anosov about the number of closed geodesics on Finsler 2-spheres. This workshop was organised by the authors. The workshop was attended by more than 50 participants from 12 countries. Contributions: \begin{itemize}\item[--]Casim Abbas (joint with Kai Cieliebak and Helmut Hofer), A new approach to the Weinstein conjecture in dimension three (p. 1747) \item[--]Alberto Abbondandolo (joint with Matthias Schwarz), On the Floer homology of cotangent bundles (p. 1749) \item[--]Sergey Bolotin, Shadowing chains of collision orbits in the elliptic 3-body problem (p. 1753) \item[--]Martin Celli, Central configurations with vanishing total mass in the 4-body problem (p. 1755) \item[--]Chong-Qing Cheng, Arnold diffusion in Hamiltonian Systems: A priori unstable case (p. 1758) \item[--]Walter Craig, KAM theory for partial differential equations (p. 1760) \item[--]L. H. Eliasson (joint with S. B. Kuksin), KAM for the nonlinear Schrödinger equation (p. 1763) \item[--]Albert Fathi, Sard, Whitney, Assouad and Mather (p. 1766) \item[--]Jacques Féjoz, About M. Herman's proof of 'Arnold's theorem' in celestial mechanics (p. 1767) \item[--]Boris Hasselblatt (joint with Patrick Foulon), Zygmund foliations and rigidity (p. 1770) \item[--]Mathilde Kammerer-Colin de Verdière (joint with Marc Chaperon), Normally hyperbolic spheres in the coupling of oscillators (p. 1773) \item[--]Anatole Katok, Two new approaches to local rigidity of abelian actions: KAM and algebraic K-theory (p. 1774) \item[--]Janko Latschev, Variation on a theorem of C. Conley (p. 1774) \item[--]Yiming Long (joint with Victor Bangert), Multiple closed geodesics on Finsler 2-spheres (p. 1777) \item[--]Ricardo Perez-Marco, Log-Riemann Surfaces (p. 1779) \item[--]Felix Schlenk (joint with Urs Frauenfelder and Leonardo Macarini), Fiberwise volume growth via Lagrangian intersections (p. 1779) \item[--]Serge Tabachnikov, Tire track geometry and flotation problems (p. 1782) \item[--]C. Eugene Wayne (joint with G. Schneider), Normal forms and the nonlinear Schrödinger approximation to water waves (p. 1784) \item[--]Joa Weber, Noncontractible periodic orbits in cotangent bundles (p. 1787) \item[--]Chris Wendl, Holomorphic foliations and 3-dimensional Reeb dynamics (p. 1790) \item[--]Lai-Sang Young (joint with Jean-Pierre Eckmann), Nonequilibrium steady-states for Hamiltonian and stochastic systems (p. 1791).\end{itemize}