reakup of shearless meanders and “outer” tori in the standard ontwist map

The breakup of shearless invariant tori with winding number = 11+ / 12+ in continued fraction representation of the standard nontwist map is studied numerically using Greene’s residue criterion. Tori of this winding number can assume the shape of meanders folded-over invariant tori which are not graphs over the x axis in x ,y phase space , whose breakup is the first point of focus here. Secondly, multiple shearless orbits of this winding number can exist, leading to a new type of breakup scenario. Results are discussed within the framework of the renormalization group for area-preserving maps. Regularity of the critical tori is also investigated. © 2006 American Institute of Physics. DOI: 10.1063/1.2338026