Summer Graduate School

The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.

Prerequisites:

Students will be expected to have had a basic course on ordinary differential equations at the level of Arnold's "Ordinary Differential Equations", as well as graduate-level courses in manifolds and differential forms. A typical first or second year graduate course at the level of Guillemin and Pollack "Differential Topology", for example, would be sufficient. Exposure to some basic dynamical systems and Hamiltonian dynamics (especially, acquaintance with Arnold's "Mathematical Methods of Classical Mechanics") would be desirable, but not assumed. The basic results from those areas needed to understand subsequent material in the summer school will be developed in the course.

Bibliography (PDF)