Author Type

Graduate Student

Date of Award

2017

Document Type

Dissertation

Publication Status

Version of Record

Submission Date

October 2026

Thesis/Dissertation Advisor [Chair]

Kalies, William D.

Thesis/Dissertation Co-Chair

Mireles-James, Jason D.

Abstract

Gravitational N-body problems are central in classical mathematical physics. Studying their long time behavior raises subtle questions about the interplay between regular and irregular motions and the boundary between integrable and chaotic dynamics. Over the last hundred years, concepts from the qualitative theory of dynamical systems such as stable/unstable manifolds, homoclinic and heteroclinic tangles, KAM theory, and whiskered invariant tori, have come to play an increasingly important role in the discussion. In the last fty years the study of numerical methods for computing invariant objects has matured into a thriving sub-discipline. This growth is driven at least in part by the needs of the world's space programs. Recent work on validated numerical methods has begun to unify the computational and analytical perspectives, enriching both aspects of the subject. Many of these results use computer assisted proofs, a tool which has become increasingly popular in recent years. This thesis presents a proof that the circular restricted four body problem is non-integrable. The proof of this result is obtained as an application of more general rigorous numerical methods in nonlinear analysis.

Extent

185 p.

Comments

Includes bibliography.|Dissertation (Ph.D.)--Florida Atlantic University, 2017.|FAU Electronic Theses and Dissertations Collection|Includes bibliography.

Identifier

FA00004997

Format

pdf

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