Irregular period-tripling bifurcations in axisymmetric scalefree potentials

We investigate the phenomenon of irregular bifurcations in axisymmetric scalefree potentials, in which a tube orbit gives rise to a new family of orbits of period 3. A proper understanding of the formation of this irregular family of orbits is important because the family occupies a fair portion of the phase space in models where it occurs. We show that these bifurcations are related to the transition of the rotation number of the phase-space torus through 1/3. This type of bifurcation is closely related to the behavior of nontwist maps.