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The Circular Restricted Four Body Problem is Non-Integrable: A Computer Assisted Proof
| Title: | The Circular Restricted Four Body Problem is Non-Integrable: A Computer Assisted Proof. |
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| Name(s): |
Kepley, Shane, author Kalies, William D., Thesis advisor Mireles-James, Jason D., Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Mathematical Sciences |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2017 | |
| Date Issued: | 2017 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 185 p. | |
| Language(s): | English | |
| Summary: | 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. | |
| Identifier: | FA00004997 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2017. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Dissertations, Academic -- Florida Atlantic University Mathematical physics. Invariants. Dynamical systems |
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| Held by: | Florida Atlantic University Libraries | |
| Sublocation: | Digital Library | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004997 | |
| Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
