Breakup of inverse golden mean shearless tori in the two-frequency standard nontwist map

Abstract

The breakup of shearless invariant tori with winding number ω = ( 5 − 1 ) / 2 (inverse golden mean) is studied using Greeneʼs residue criterion in the recently derived two-frequency or extended standard nontwist map (ESNM). Depending on the frequency ratio, the ESNM has or does not have a particular spatial symmetry. If the symmetry is present, the breakup is shown to be the same as in the standard nontwist map; if not, the results are very different. ► We study the breakup of shearless invariant tori with inverse golden mean winding number in an area-preserving nontwist map perturbed by two harmonics. ► Torus breakup is studied using Greeneʼs residue criterion. ► Symmetry of the map (or lack of) is found to affect the details of the breakup.