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

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.

Text AmnaShaddadThesisFinal.pdf Download (1MB)

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)
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:	https://eprints.maths.manchester.ac.uk/id/eprint/2710

Actions (login required)

View Item