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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

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.

Identiferoai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:764584
Date January 2018
CreatorsShaddad, Amna
ContributorsMuldoon, Mark ; Montaldi, James
PublisherUniversity of Manchester
Source SetsEthos UK
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation
Sourcehttps://www.research.manchester.ac.uk/portal/en/theses/the-classification-and-dynamics-of-the-momentum-polytopes-of-the-su3-action-on-points-in-the-complex-projective-plane-with-an-application-to-point-vortices(456a7a49-ef1b-4660-a8e6-8d4cd0791d9d).html

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