Bifurcations and linear stability of families of relative equilibria with a dominant vortex
2014-07
Loading...
View/Download File
Persistent link to this item
Statistics
View StatisticsJournal Title
Journal ISSN
Volume Title
Title
Bifurcations and linear stability of families of relative equilibria with a dominant vortex
Authors
Published Date
2014-07
Publisher
Type
Thesis or Dissertation
Abstract
Studying the dynamics of vortex configurations with one large vortex with and N smaller vortices has applications to physical electromagnetic systems and atmospheric science, as well as being a historically interesting problem. The existence, and linear stability of relative equilibria configurations of the (1+N)-vortex problem are examined. Such configurations are shown to be critical points of a special potential function, and their linear stability depends on the weighted Hessian of this potential. Algebraic geometry and some numerical methods are used to examine the bifurcations of critical points and stability specifically in the case of N=3.
Keywords
Description
University of Minnesota Ph.D. dissertation. July 2014. Major: Mathematics. Advisor: Richard Moeckel. 1 computer file (PDF); vii, 88 pages, appendices A-C.
Related to
Replaces
License
Collections
Series/Report Number
Funding information
Isbn identifier
Doi identifier
Previously Published Citation
Suggested citation
Hoyer-Leitzel, Alanna. (2014). Bifurcations and linear stability of families of relative equilibria with a dominant vortex. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/165418.
Content distributed via the University Digital Conservancy may be subject to additional license and use restrictions applied by the depositor. By using these files, users agree to the Terms of Use. Materials in the UDC may contain content that is disturbing and/or harmful. For more information, please see our statement on harmful content in digital repositories.