Hamiltonian Systems and Celestial Mechanics (15w5010)

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


(University of Victoria)

(Universidad Autonoma de Barcelona)

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


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