A Poincaré-Birkhoff Theorem for 3-Dimensional Energy Levels

Abstract: In subcritical energy levels of the planar circular restricted 3-body problem (PCR3BP) Poincaré encountered special periodic orbits that span an annular global section for the flow. This motivated the formulation of what is known today as the Poincaré-Birkhoff theorem, from where Poincaré derived beautiful applications to the PCR3BP. In this talk I would like to explain how the action functional from classical mechanics can be used to prove analogous statements for more general systems. This is based on joint work with Al Momin and Pedro Salomão (NYU-Shanghai).