  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.
