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Chaos in a model of the forced and damped sine-Gordon equation

Citation

Kovacic, Gregor (1990) Chaos in a model of the forced and damped sine-Gordon equation. Dissertation (Ph.D.), California Institute of Technology. http://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.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Wiggins, Stephen R.
Thesis Committee:
  • Unknown, Unknown
Defense Date:26 September 1989
Record Number:CaltechETD:etd-05152007-075202
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-05152007-075202
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:26 Dec 2012 02:42

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