Castro, Sofia Balbina Santos Dias de (1993) Mode interactions with symmetry. PhD thesis, University of Warwick.

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Abstract

This thesis deals with steady-state mode interaction problems with symmetry. We prove several results concerning problems invariant under the action of an arbitrary compact Lie group Γ. These include the existence of mixed-mode solutions and secondary Hopf bifurcations. We also consider the unfolding of the equations characterizing such problems. Where appropriate, we distinguish the case when Γ acts trivially on one of the modes. We then apply the results to the problems of the (1,3)-, (1,5)- and (1,3,5)-mode interactions with spherical symmetry. We also consider the (3,5)- and the (1,3,5)-mode interaction problems with SO(3) symmetry.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Lie groups, Bifurcation theory, Spherical harmonics, Symmetry (Mathematics)
Date:	February 1993
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Stewart, Ian, 1945-
Sponsors:	Junta Nacional de Investigação Científica e Tecnológica (Portugal) (JNICT)
Extent:	viii, 109 p.
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/4041

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