AREA-PRESERVING NONTWIST MAPS - PERIODIC-ORBITS AND TRANSITION TO CHAOS

Area preserving nontwist maps, i.e. maps that violate the twist condit ion, are considered. A representative example, the standard nontwist m ap that violates the twist condition along a curve called the shearles s curve, is studied in detail. Using symmetry lines and involutions, p eriodic orbits are computed and two bifurcations analyzed: periodic or bit collisions and separatrix reconnection. The transition to chaos du e to the destruction of the shearless curve is studied. This problem i s outside the applicability of the standard KAM (Kolmogorov-Arnold-Mos er) theory. Using the residue criterion we compute the critical parame ter values for the destruction of the shearless curve with rotation nu mber equal to the inverse golden mean. The results indicate that the d estruction of this curve is fundamentally different from the destructi on of the inverse golden mean curve in twist maps. It is shown that th e residues converge to a six-cycle at criticality.