Renormalization and Transition to Chaos in Area Preserving Nontwist Maps
نویسندگان
چکیده
The problem of transition to chaos, i.e. the destruction of invariant circles or KAM (Kolmogorov-Arnold-Moser) curves, in area preserving nontwist maps is studied within the renormalization group framework. Nontwist maps are maps for which the twist condition is violated along a curve known as the shearless curve. In renormalization language this problem is that of nding and studying the xed points of the renormalization group operator R that acts on the space of maps. A simple period-two xed point of R, whose basin of attraction contains the nontwist maps for which the shearless curve exists, is found. Also, a critical period-twelve xed point of R, with two unstable eigenvalues, is found. The basin of attraction of this critical xed point contains the nontwist maps for which the shearless curve is at the threshold of destruction. This basin deenes a new universality class for the transition to chaos in area preserving maps.
منابع مشابه
Area preserving nontwist maps: periodic orbits and transition to chaos
Area preserving nontwist maps, i.e. maps that violate the twist condition, are considered. A representative example, the standard nontwist map that violates the twist condition along a curve called the shearless curve, is studied in detail. Using symmetry lines and involutions, periodic orbits are computed and two bifurcations analyzed: periodic orbit collisions and separatrix reconnection. The...
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