  For resonant slow extraction of accelerated particle beams from synchrotrons,
a 3rd order resonance driven by sextupole magnets is commonly used. This note
reviews the non-linear particle dynamics under these conditions as described by
the Kobayashi Hamiltonian, focussing on the amplitude and phase dependent
detuning. Using the Kobayashi Hamiltonian as the invariant, an expression for
the action and the average detuning as a function of the Hamiltonian is derived
and compared to numerically obtained results.
