Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map

Details Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map

2006-01-18

arxiv.org/abs/nlin/0601040v1

Nonlinear Sciences

Chaotic Dynamics

submitted to Chaos

Scientific paper

10.1063/1.2338026

The breakup of shearless invariant tori with winding number $\omega=[0,1,11,1,1,...]$ (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.

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