- 98-357 Chandre C., Jauslin H.R., Benfatto G.
- An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems
May 22, 98
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Abstract. We construct an approximate renormalization scheme for Hamiltonian
systems with two degrees of freedom. This scheme is a combination of
Kolmogorov-Arnold-Moser (KAM) theory
and renormalization-group techniques. It makes the connection between the
approximate renormalization procedure derived by Escande and Doveil, and
a systematic expansion of the transformation. In particular, we show that
the two main approximations, consisting in keeping only the quadratic
terms in the actions and the two main resonances, keep the essential
information on the threshold of the breakup of invariant tori.