Lei Zhao (Augsburg)
J^+-Invariants for two-center Stark-Zeeman systems
Abstract:
For immersed curves in the plane, Arnold has defined three invariants in which the J^+-invariant has been adapted by Cieliebak-Frauenfelder-van Koert in 2017 to two invariants for periodic orbits of (one-center) Stark-Zeeman systems which includes the two-center problem and the restricted three-body problem as examples. These invariants are invariant under homotopy along generic family of periodic orbits of Stark-Zeeman systems. In this talk I will recall their construction, as well as explain an extension, jointly with K. Cieliebak and U. Frauenfelder, for Stark-Zeeman systems with two Newtonian/Coulombian singularities, in which case we obtain four J^+-like invariants, based on Levi-Civita and Birkhoff regularizations.