Computer Assisted Proof of Drift Orbits Along Normally Hyperbolic Manifolds II: Application to the Restricted Three Body Problem

TL;DR

This paper provides a computer-assisted proof of diffusion orbits in the Planar Elliptic Restricted Three Body Problem, demonstrating energy changes through shadowing along normally hyperbolic manifolds.

Contribution

It introduces a novel method for proving diffusion orbits in the elliptic problem as a perturbation of the circular case, with explicit energy change results.

Findings

Existence of diffusion orbits with explicit energy changes

Applicable for small eccentricity perturbations

Method based on shadowing along stable/unstable manifold intersections

Abstract

We present a computer assisted proof or diffusion in the Planar Elliptic Restricted Three Body Problem. We treat the elliptic problem as a perturbation of the circular problem, where the perturbation parameter is the eccentricity of the primaries. The unperturbed system preserves energy, and we show that for sufficiently small perturbations we have orbits with explicit energy changes, independent from the size of the perturbation. The result is based on shadowing of orbits along transversal intersections of stable/unstable manifolds of a normally hyperbolic cylinder.