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Complex bifurcation

Citation

Henderson, Michael E. (1985) Complex bifurcation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-03262008-112516

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Real equations of the form [...] = 0 are shown to have a complex extension [...] = 0, defined on the complex Banach space [...]. At a singular point of the real equation this extension has solution branches corresponding to both the real and imaginary roots of the Algebraic Bifurcation Equations (ABE's). We solve the ABE's at simple quadratic folds, quadratic bifurcation points, and cubic bifurcation points, and show that these are complex bifurcation points. We also show that at a Hopf bifurcation point of the real equation there are two families of complex periodic orbits, parametrized by three real parameters. By taking sections of solutions of complex equations with two real parameters, we show that complex branches may connect disjoint solution branches of the real equation. These complex branches provide a simple and practical means of locating disjoint branches of real solutions. Finally, we show how algorithms for computing real solutions may be modified to compute complex solutions. We use such an algorithm to find solutions of several example problems, and locate two sets of disjoint real branches.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Keller, Herbert Bishop
Thesis Committee:
  • Unknown, Unknown
Defense Date:28 September 1984
Record Number:CaltechETD:etd-03262008-112516
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-03262008-112516
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1159
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:04 Apr 2008
Last Modified:06 Feb 2013 23:27

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