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

TL;DR

This paper introduces new J+-like invariants for periodic orbits in planar two-center Stark-Zeeman systems, extending previous work and analyzing their independence through a novel interior connected sum construction.

Contribution

It defines four new invariants for two-center Stark-Zeeman systems and explores their relationships, expanding the understanding of these dynamical systems.

Findings

The invariants are largely independent.

The invariants are constructed using Levi-Civita and Birkhoff regularizations.

A new interior connected sum construction is introduced.

Abstract

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.