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 a planar one-center Stark-Zeeman system in [K. Cieliebak, U. Frauenfelder and O. van Koert. Periodic orbits in the restricted three-body problem and Arnold's J(+)-invariant. Regul. Chaotic Dyn. 22(4) (2017), 408-434] 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.