Citation
Kovacic, Gregor (1990) Chaos in a model of the forced and damped sine-Gordon equation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rg86-2095. https://resolver.caltech.edu/CaltechETD:etd-05152007-075202
Abstract
We analytically determine two of the mechanisms which cause chaotic dynamics to appear in a model of the forced and damped Sine-Gordon equation. In particular, we find orbits homoclinic to periodic orbits, and orbits homoclinic to fixed points which satisfy conditions sufficient to guarantee the existence of nearby chaotic invariant sets. One of these homoclinic orbits is a so-called Silnikov-type loop. A proof the existence of a symmetric pair of such loops is our main result. This proof consists of a modified Melnikov perturbation analysis, augmented by some techniques from the field of geometric singular perturbation theory.
| Item Type: | Thesis (Dissertation (Ph.D.)) |
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| Degree Grantor: | California Institute of Technology |
| Division: | Engineering and Applied Science |
| Major Option: | Applied And Computational Mathematics |
| Thesis Availability: | Public (worldwide access) |
| Research Advisor(s): |
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| Thesis Committee: |
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| Defense Date: | 26 September 1989 |
| Record Number: | CaltechETD:etd-05152007-075202 |
| Persistent URL: | https://resolver.caltech.edu/CaltechETD:etd-05152007-075202 |
| DOI: | 10.7907/rg86-2095 |
| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. |
| ID Code: | 1818 |
| Collection: | CaltechTHESIS |
| Deposited By: | Imported from ETD-db |
| Deposited On: | 23 May 2007 |
| Last Modified: | 19 Apr 2021 22:25 |
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