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 2sphere. 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 twovortex systems.
Date of Award  31 Dec 2018 

Original language  English 

Awarding Institution   The University of Manchester


Supervisor  Mark Muldoon (Supervisor) & James Montaldi (Supervisor) 

 relative equilibria
 special unitary group
 momentum polytopes
 vortices
 complex projective space
 hamiltonian action
 lie algebra
 lie groups
 differential geometry
 Weyl Chamber
 geometric mechanics
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, A. (Author). 31 Dec 2018
Student thesis: Phd