$J^+$-like invariants of periodic orbits of the second kind 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.