  We study the dynamics near the truncated p : +/- q resonant Hamiltonian
equilibrium for p, q coprime. The critical values of the momentum map of the
Liouville integrable system are found. The three basic objects reduced period,
rotation number, and non-trivial action for the leading order dynamics are
computed in terms of complete hyperelliptic integrals. A relation between the
three functions that can be interpreted as a decomposition of the rotation
number into geometric and dynamic phase is found. Using this relation we show
that the p : -q resonance has fractional monodromy. Finally we prove that near
the origin of the 1 : -q resonance the twist vanishes.
