Existence of a Center Manifold in a Practical Domain around L1 in the Restricted Three Body Problem

TL;DR

This paper proves the existence of center manifolds in large regions around L1 in the planar Restricted Three Body Problem using a combination of topological, normal form, and computer-assisted methods.

Contribution

It provides a rigorous proof of a center manifold's existence in a practical domain for the Restricted Three Body Problem, with explicit region characterization.

Findings

Existence of a center manifold near L1 confirmed.

Explicit domain where the center manifold exists identified.

Method combines topological, normal form, and computer-assisted techniques.

Abstract

We give a proof of existence of centre manifolds within large domains for systems with an integral of motion. The proof is based on a combination of topological tools, normal forms and rigorous-computer-assisted computations. We apply our method to obtain an explicit region in which we prove existence of a center manifold in the planar Restricted Three Body Problem.