IAM-PIMS-MITACS Distinguished Colloquium: Richard Montgomery

Abstract:

A brake orbit for the Newtonian three-body problem is a solution for which all three velocities are zero at some instant: the brake instant. If we follow such an orbit there will be a later instant at which the three bodies become colinear: the instant of syzygy. In this manner we can define a flow-induced "Poincare map" from brake initial conditions to syzygy configurations. Appropriately viewed, this brake-to-syzygy map is a map between planar domains. Understanding its image destroyed certain myths that the speaker had regarding action-minimizing orbits. The map fits in towards a possible global understanding of the planar three-body problem which we will explain. Key is a viewpoint on the planar three-body problem in which the configuration of all three bodies is represented as a single point in 3-space (its "shape") and in which Newton's equations become a mechanical system on this 3-space. Some movies of Paul Klee-like periodic brake orbits inspired by this work will be shown.