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 T¹ 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 T¹ action. Thus we demonstrate that, given a Tⁿ⁻¹ invariant Hamiltonian H, it is the Tⁿ⁻¹ action, rather than H, that determines monodromy.

Duke Scholars

Author Konstantinos Efstathiou DKU Faculty