$J^{+}$-invariants for planar two-center Stark-Zeeman systems

In this paper, we introduce the notion of planar two-center Stark- Zeeman systems and define four J±like invariants for their periodic orbits. The construction is based on a previous construction for planar one-center Stark-Zeeman system in [Cieliebak-Frauenfelder-van Koert 2017] as well as Levi-Civita and Birkhoff regularizations. We analyze the relationship among these invariants and show that they are largely independent, based on a new construction called interior connected sum.