Recent Progress in Classical Mechanics

The goal of this lecture is to review several developments in classical mechanics that have taken place in the last years, that will fit in the time of the talk and that I have become aware of. Unfortunately, the latter is a constraint more severe than what I would like and I apologize to the authors and the audience for many things that have been left out. In particular, I have left out topics such as “twist mappings”, “geometric quantization” or “geometric phases” and “quantum chaos” that are generating a great deal of activity in the literature. I would also like to recommend the excellent set of reviews [AANS] for the many developments that took place up to the time the books were published.