  The presence of focus-focus singularities in semi-toric integrables
Hamiltonian systems is one of the reasons why there cannot exist global
Action-Angle coordinates on such systems. At focus-focus critical points, the
Liouville-Arnold-Mineur theorem does not apply. In particular, the affine
structure of the image of the moment map around has non-trivial monodromy. In
this article, we establish that the singular behaviour and the multi-valuedness
of the Action integrals is given by a complex logarithm. This extends a
previous result by Vu Ngoc to any dimension. We also calculate the monodromy
matrix for these systems.
