Phase space (left) and winding number profile along (right) of two stages of the odd-period (standard) reconnection sequence. The ranges of all plots are identical. Parameters were chosen (a) slightly before collision and (b) slightly after collision of two major odd-period orbit chains (winding number marked by dashed lines).
Parameter space overview of SNM, with higher orbit branching points, bifurcation (collision) curves, and approximate reconnection thresholds for odd-period orbits and . Bifurcation curves for even-period orbits , , and and the breakup boundary for the central shearless tori are indicated. New points are marked by two circles. (☉ denotes outer shearless curve, all others are central ones.)
of differences in approximating the critical central shearless meander at on .
Residue six-cycles for orbits at meander breakup. Cycles for orbits on are the same, with up and down interchanged. Cycles on are shifted by three, with up and down interchanged. Cycles on are shifted by three.
Phase space at the meander breakup, and . Also shown are the symmetry lines , , , and .
Two levels of magnification, in symmetry line coordinates , of the central shearless meander at breakup. Also shown are the nearby up and down orbits of the th (top) and th (bottom) continued fraction convergents.
values in phase space of the , , , and outer orbits on the symmetry line as a function of , at .
differences in approximating the critical shearless outer orbits at on the (above) and (below) symmetry lines.
Residue behavior for orbits on to at the breakup of outer shearless tori. Residues for assumed breakup parameter values are indicated by the bold line. Residues for five parameter values with in steps of are indicated by thin lines and residues for five parameter values with in steps of by dotted lines.
Phase space of the outer shearless tori at breakup, where and . The symmetry lines to are shown.
The hull functions (left) and (right) for the critical central and outer meanders.
The plot of vs for the hull functions.
Continued fraction convergents for , where (following the notation of Refs. 3 and 4 ).
Period-six convergence pattern of residues near criticality on different symmetry lines (following the notation of Ref. 3 ). Symmetry properties of the SNM further imply , , , , , .
Numerical values of the critical parameters in the vicinity of the shearless outer tori breakup, with the conjectured critical parameters shown in Italics.
The regularities of hull functions (top) and (bottom), found using the slopes of lines in Fig. 12 .
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