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

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

2006-07-12

arxiv.org/abs/nlin/0607021v1

Nonlinear Sciences

Chaotic Dynamics

4 pages, 5 figures

Scientific paper

10.1016/j.physleta.2007.02.054

The breakup of the shearless invariant torus with winding number $\omega=\sqrt{2}-1$ 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.

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