Lei Zhao (Chern Institute of Mathematics, Nankai University)
Convex Embedding in the rotating Kepler problem and the Birkhoff conjecture
In this talk, I shall show that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surfaces of the planar rotating Kepler problem into R4 endowed with its standard symplectic structure. A direct consequence is the dynamical convexity of the planar rotating Kepler problem, which has been established by Albers-Fish-Frauenfelder-van Koert by direct computations. I shall also explain its relationship with the Birkhoff conjecture about the existence of a global surface of section in the restricted planar circular three body problem.
This work is a result from a collaboration with Urs Frauenfelder (Augsburg) and Otto van Koert (Seoul).