Breakup of shearless invariant tori in cubic and quartic nontwist maps

The effect of symmetry on invariant torus breakup in nontwist maps is investigated. In particular, the breakup of shearless invariant tori with winding number ω = ( 5 - 1 ) / 2 (inverse golden mean) and ω = 2 - 1 (an inverse silver mean) is studied numerically using Greene’s residue criterion in a cubic and a quartic nontwist map. The details of the breakup are compared to those previously obtained for the standard nontwist map, which has the same particular spatial symmetry as the quartic map. The cubic map lacks this symmetry. The results show that if the symmetry exists, the details of the breakup are the same as in the standard nontwist map. If the symmetry does not exist, the breakup is shown to be different.