Kolmogorov-Arnold-Moser--Renormalization-Group Analysis of Stability in Hamiltonian Flows

Details Kolmogorov-Arnold-Moser--Renormalization-Group Analysis of Stability in Hamiltonian Flows Kolmogorov-Arnold-Moser--Renormalization-Group Analysis of Stability in Hamiltonian Flows

1998-02-25

arxiv.org/abs/chao-dyn/9802021v1

Phys. Rev. Lett. 79, 3881 (1997)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures, RevTex

Scientific paper

10.1103/PhysRevLett.79.3881

We study the stability and breakup of invariant tori in Hamiltonian flows using a combination of Kolmogorov-Arnold-Moser (KAM) theory and renormalization-group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyze the strong coupling regime. We show that the KAM iteration converges up to the critical coupling at which the torus breaks up. Adding a renormalization consisting of a rescaling of phase space and a shift of resonances allows us to determine the critical coupling with higher accuracy. We determine a nontrivial fixed point and its universality properties.

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