Dynamische Systeme

Abstract

This workshop, organised by Hakan Eliasson (Paris), Helmut Hofer (New York), and Jean-Christophe Yoccoz (Paris) continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser & Zehnder meeting” in 1981. The workshop was attended by more than 50 participants from 12 countries. The main themes of the workshop were the new results and developments in the area of classical dynamical systems, in particular in celestial mechanics and Hamiltonian systems. The workshop covers a large area of dynamical systems and the following samples give an idea about the scope. The topic of Arnold Diffusion was treated in great detail by talks of M. Levi and J. Mather. In the classical field of celestial mechanics new insight has been gained about two interesting families of relative periodic solutions of the spatial n-body problem (the $P_{12}$-family and the hip-hop-family) as they share the property of being global continuations of Lyapunov families which bifurcate from a relative equilibrium solution in the direction orthogonal to the plane of motion (A. Chenciner). K. Kuperberg reported on the construction of flows on three-manifolds where every nonconstant trajectory is wild in a sense related to the Artin–Fox example of an exotic arc in Euclidean three-space. Other results were concerned with one of the main problems in Hamiltonian dynamic, namely the stability of motions in nearly-integrable systems (L. Niedermann). Y. Pesin outlined the construction of hyperbolic volume-preserving flows on manifolds of dimension at least three and V. Ginzburg described the recent developments concerning the Conley Conjecture for periodic points of Hamiltonian symplectic maps. John Franks described his recent results about group actions on surfaces. In addition several talks covered new Floer-theoretic methods in the study of Hamiltonian systems and it will be interesting to see in the future how these symplectic methods can be merged with the more classical dynamical systems methods.