Convexity Of Singular Affine Structures And Toric-Focus Integrable Hamiltonian Systems

A systematic study of symplectic convexity for integrable Hamiltonian systems with elliptic and focus-focus singularities. Peculiarly, these systems’ base spaces are still smooth manifolds, analogous to the toric case, but their associated integral affine structures are singular, with non-trivial monodromy, due to focus singularities.