Lyapunov Orbits at L2 and Transversal Intersections of Invariant Manifolds in the Jupiter-Sun Planar Restricted Circular Three Body Problem

TL;DR

This paper proves the existence of Lyapunov orbits at L2 in the Jupiter-Sun system and demonstrates transversal intersections of their invariant manifolds, providing explicit bounds through computer-assisted methods.

Contribution

It offers a computer-assisted proof of Lyapunov orbits at L2 and their transversal manifold intersections with explicit bounds, advancing dynamical systems analysis in celestial mechanics.

Findings

Existence of Lyapunov orbits from L2 to halfway to the smaller primary.

Transversal intersections of invariant manifolds near orbits with energies close to comet Oterma.

Explicit bounds on intersection location and angles.

Abstract

We present a computer assisted proof of existence of a family of Lyapunov orbits which stretches from L2 up to half the distance to the smaller primary in the Jupiter-Sun planar restricted circular three body problem. We then focus on a small family of Lyapunov orbits with energies close to comet Oterma and show that their associated invariant manifolds intersect transversally. Our computer assisted proof provides explicit bounds on the location and on the angle of intersection.