On a new fixed point of the renormalization group operator for area-preserving maps

The breakup of the shearless invariant torus with winding number omega = root 2 - 1 is studied numerically using Greene's residue criterion in the standard nontwist map. The residue behavior and parameter scaling at the breakup suggests the existence of a new fixed point of the renormalization group operator (RGO) for area-preserving maps. The unstable eigenvalues of the RGO at this fixed point and the critical scaling exponents of the torus at breakup are computed. (C) 2007 Elsevier B.V. All rights reserved.