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

Arriving in Banff, Alberta Sunday, January 13 and departing Friday January 18, 2013

## Organizers

(Università ROMA TRE)

(University of Maryland)

John Mather (Princeton University)

(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;