Monodromy of Hamiltonian systems with complexity 1 torus actions

We consider the monodromy of n-torus bundles in n degree of freedom integrable Hamiltonian systems with a complexity 1 torus action, that is, a Hamiltonian Tn-1 action. We show that orbits with T-1 isotropy are associated to non-trivial monodromy and we give a simple formula for computing the monodromy matrix in this case. In the case of 2 degree of freedom systems such orbits correspond to fixed points of the T-1 action. Thus we demonstrate that, given a Tn-1 invariant Hamiltonian H, it is the Tn-1 action, rather than H, that determines monodromy. (C) 2016 Elsevier B.V. All rights reserved.