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Nonlinear Phenomena from a Reinjected Horseshoe
| Title: | Nonlinear Phenomena from a Reinjected Horseshoe. |
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| Name(s): |
Fontaine, Marcus, author Kalies, William D., Thesis advisor Naudot, Vincent, 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: | 2016 | |
| Date Issued: | 2016 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 86 p. | |
| Language(s): | English | |
| Summary: | A geometric model of a reinjected cuspidal horseshoe is constructed, that resembles the standard horseshoe, but where the set of points that escape are now reinjected and contribute to richer dynamics. We show it is observed in the unfolding of a three-dimensional vector field possessing an inclination-flip homoclinic orbit with a resonant hyperbolic equilibrium. We use techniques from classical dynamical systems theory and rigorous computational symbolic dynamics with algebraic topology to show that for suitable parameters the flow contains a strange attractor. | |
| Identifier: | FA00004591 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2016. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Nonlinear theories. Computational dynamics. Attractors (Mathematics) Chaotic behavior in systems. Mathematical physics. |
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| Held by: | Florida Atlantic University Libraries | |
| Sublocation: | Digital Library | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004591 | |
| 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. |
