Shaddad, Amna
(2018)
*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.*
Doctoral thesis, University of Manchester.

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## Abstract

We have fully classified the momentum polytopes of the SU(3) action on CP2 x CP2 and CP2 x CP2 x CP2, both actions with weighted symplectic forms, and their corresponding transition momentum polytopes. For CP2 x CP2 the momentum polytopes are distinct line segments. The action on CP2 x CP2 x CP2 has 8 different momentum polytopes. The vertices of the momentum polytopes of the SU(3) action on CP2 x CP2 x CP2 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.

Item Type: | Thesis (Doctoral) |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems |

Depositing User: | Dr James Montaldi |

Date Deposited: | 15 May 2019 17:17 |

Last Modified: | 15 May 2019 17:17 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/2710 |

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