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Title: The classification and dynamics of the momentum polytopes of the SU(3) action on points in the complex projective plane with an application to point vortices
Author: Shaddad, Amna
ISNI:       0000 0004 7656 876X
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2018
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We have fully classified the momentum polytopes of the SU(3) action on CP(2)xCP(2) and CP(2)xCP(2) xCP(2), both actions with weighted symplectic forms, and their corresponding transition momentum polytopes. For CP(2)xCP(2) the momentum polytopes are distinct line segments. The action on CP(2)xCP(2) xCP(2), has 9 different momentum polytopes. The vertices of the momentum polytopes of the SU(3) action on CP(2)xCP(2) xCP(2), fall into two categories: definite and indefinite vertices. The reduced space corresponding to momentum map image values at definite vertices is isomorphic to the 2-sphere. We show that these results can be applied to assess the dynamics by introducing and computing the space of allowed velocity vectors for the different configurations of two-vortex systems.
Supervisor: Muldoon, Mark ; Montaldi, James Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: hamiltonian action ; special unitary group ; vortices ; relative equilibria ; momentum polytopes ; differential geometry ; Weyl Chamber ; lie algebra ; lie groups ; geometric mechanics ; complex projective space