# Hamiltonian Systems and Celestial Mechanics (15w5010)

Arriving in Oaxaca, Mexico Sunday, September 6 and departing Friday September 11, 2015

## Organizers

(University of Victoria)

Ernesto Perez-Chavela (Instituto Tecnológico Autónomo de México (ITAM))

## Objectives

We will bring together experts in celestial mechanics and Hamiltonian systems, whose work touches on various aspects of dynamics, such as variational methods, Aubrey-Mather theory, and ergodic theory. Our goal is to build a theoretical framework suitable to attack some of the many unsolved question of the $N$-body problem and to see how they can further the general field of Hamiltonian systems. Such an event will help the community undertake the following research directions:

- coexistence of stable and unstable regions

- analysis of mean-orbital 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

- applications of Aubry-Mather theory to the study of bounded and parabolic orbits

- applications of weak KAM and Nekhoroshev theory to the classical and the curved $N$-body problem

- stability of periodic trajectories found by variational methods

- regularization of collisions via new methods, such as the Ligon-Schaaf technique