On invariants of families of lemniscate motions in the two-center problem

TL;DR

This paper computes four topological invariants related to lemniscate motions in the two-center problem, extending Arnold's $J^+$-invariant to this specific dynamical system.

Contribution

It introduces the calculation of four topological invariants for lemniscate motions in the two-center problem, building on Arnold's $J^+$-invariant.

Findings

Four topological invariants determined for lemniscate motions

Extension of Arnold's $J^+$-invariant to this context

Provides new tools for analyzing periodic motions in celestial mechanics

Abstract

We determine four topological invariants introduced by Cieliebak-Frauenfelder-Zhao, based on Arnold's $J^+$-invariant, of periodic lemniscate motions in Euler's two-center problem.