$J^+$-like invariants of periodic orbits of the second kind in the restricted three body problem

TL;DR

This paper computes three topological invariants for certain periodic orbits in the restricted three-body problem, enhancing understanding of their qualitative behavior near the primary body when the mass ratio is small.

Contribution

It introduces the calculation of Arnold's J^+ and two other invariants for second-kind periodic orbits in the restricted three-body problem with small mass ratio.

Findings

Computed J^+, J_1, and J_2 invariants for specific periodic orbits.

Provides new insights into the topology of orbits near the primary.

Extends previous invariants analysis to second-kind orbits in the restricted three-body problem.

Abstract

We determine three invariants: Arnold's $J^+$-invariant as well as $\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near the heavier primary in the restricted three-body problem, provided that the mass ratio is sufficiently small.