Describing semi-toric critical values

For a toric integrable Hamiltonian system (IHS) with n degrees of freedom, the image of the moment map F is a n-dimensional rational convex polytope.

This is no longer the case when we deal with semi-toric IHS. Yet we can recover a nice description of the image of the moment map for these systems. This requires a good description of the locci of semi-toric critical values.

One way of doing so is by using the local model existing for

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This is a convex set !

An Atiyah - Guillemin & Sternberg theorem for semi-toric systems

Given a Hamiltonian action of a k-torus T on a symplectic manifold M of dimension 2n with moment map J:M --> R^k, a theorem discovered by Atiyah, and by Guillemin & Sternberg independently, states tha

Asymptotics of Action variables near semi-toric singularities

Near singularities with focus-focus components, the Lagrangian torus foliation given by a semi-toric integrable Hamiltonian system is pinched. At the critical leaf, one can't define a complete set of