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

  • Amna Shaddad

Student thesis: Phd


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.
Date of Award31 Dec 2018
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorMark 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

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