New Perspectives on the $N$-body Problem (13w5055)

Arriving Sunday, January 13 and departing Friday January 18, 2013

Organizers

Luigi Chierchia (Università ROMA TRE)
Vadim Kaloshin (University of Maryland)
John Mather (Princeton University)
Susanna Terracini (Università di Torino)

Objectives

The workshop will be the ideal place where to discuss and bring up new ideas onto this subject. Our aim is to bring the main specialists of the $N$--body problem together with the leaders of different areas in dynamical systems (Variational Methods, Mather Theory, Hamiltonian dynamics, Ergodic Theory) trying to build a theoretical framework suitable to attack some of the many unsolved aspects of the $N$--body problem.

In our opinion, gathering together the proposed participants will be extremely helpful in undertaking the following directions:


  • coexistence of stable and unstable regions;
  • analysis of meanorbital resonances;
  • Nekhoroshev analysis of the secular approximate invariants (mutual inclinations and eccentricities);
  • long-period periodic orbits near invariant tori; intermediate stable/unstable invariant tori; resonant
  • tori;
  • instabilities (including special instances of Arnold diffusion), possible applications of Aubry--Mather theory
  • symbolic dynamics;
  • study of selected trajectories such as periodic, bounded and parabolic orbits;
  • possible applications of weak KAM theory to the $N$-body problem;
  • stability issues for periodic trajectories found by variational methods;
  • regularization of collisions, absence of collisions;