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

Abstract

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.

4 pages, 5 figures

References in corpus (2)

• Renormalization and destruction of $1/{\gamma }^2$ tori in the standard nontwist map
• Breakup of Shearless Meanders and "Outer" Tori in the Standard Nontwist Map