IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

In this talk, I will describe the global dynamics of the spatial isosceles three-body problem, using ideas from Embedded Contact Homology. For energies below the critical level, the flow admits a disk-like global surface of section bounded by the Euler orbit. I will explain how estimates for the contact volume of the energy surface and for the rotation number of the Euler orbit, together with a refinement of Hutchings’ mean action theorem, force the existence of infinitely many periodic orbits and constrain their relative winding via a non-trivial twist interval. For energies above the critical level, for which the energy surface is unbounded, I will briefly discuss how the twist near infinity leads to the existence of infinitely many periodic and parabolic trajectories. This is joint work with Xijun Hu, Lei Liu, Yuwei Ou, and Zhiwen Qiao.