Speaker: Hans Koch (UT, Austin)
Title: Renormalization and Hamiltonian Flows
Abstract:
Among the most visible landmarks in Hamiltonian dynamics are groups of periodic and quasiperiodic orbits, whose rotation numbers satisfy simple arithmetic relations. These orbits also plays an important role in the study of stability questions. Renormalization allows for a detailed study of such orbit structures, by taking advantage of the underlying arithmetic properties. We will describe the main ideas of this approach, and some recent work related to the breakup of invariant tori.