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

Abstract

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.

submitted to Chaos

References in corpus (1)

• Renormalization and destruction of $1/{\gamma }^2$ tori in the standard nontwist map

Cited by in corpus (3)

• Gauss map and Lyapunov exponents of interacting particles in a billiard
• On a new fixed point of the renormalization group operator for area-preserving maps
• Boundaries of Siegel disks - numerical studies of their dynamics and regularity