97-309 Govin M., Chandre C., Jauslin H.R.

KAM-Renormalization Group Analysis of Stability in Hamiltonian Flows (88K, Postscript) Jun 3, 97

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Abstract. We study the stability and break-up of invariant tori in Hamiltonian flows using a combination of KAM theory and renormalization group techniques. We implement the scheme numerically for a family of Hamiltonians quadratic in the actions to analyse 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 scheme consisting of a rescaling of phase space and a shift of the relevant resonances, we obtain a much more efficient method that allows to determine the critical coupling with high accuracy. The results indicate that this approach captures the essential physical mechanism of the break-up of invariant tori. We determine a non-trivial fixed point of the renormalization transformation, and discuss the associated universality properties.

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