Speaker : Professor H. Scott Dumas (University of Cincinnati & University of New Mexico)
Title : What's So Great About KAM Theory?
Time : 2020-01-09 (Thu) 15:00 - 16:00
Place : Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: ``KAM" stands for mathematicians A.N. Kolmogorov, V.I. Arnold, and J.K. Moser. In classical finite-dimensional Hamiltonian systems, KAM theory guarantees the persistence of integrable-like behavior in perturbations of integrable systems. In particular, the theory guarantees the persistence of ``invariant tori" containing ``quasiperiodic solutions". Mention of the KAM theorem is often accompanied by the adjective ``celebrated"; in the 20th century, it was occasionally even called the theorem of the century. Yet KAM theory also has detractors who say it is overrated, not as deep or as useful as claimed. Between these two poles of opinion lie many mathematicians and physicists who are simply unfamiliar with KAM theory or its implications. In this mostly non-technical talk, I will give a brief overview of KAM theory, its history and its ramifications, and if time permits, I'll present some of the arguments for and against its significance and usefulness in celestial mechanics, statistical physics, and particle accelerator beam dynamics.