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An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems

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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.

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Authors and Affiliations

  1. Laboratoire de Physique, CNRS, Université de Bourgogne, BP 400, F-21011, Dijon, France

    C. Chandre & H. R. Jauslin

  2. Dipartimento di Matematica, Università di Roma “Tor Vergata,”, I-00133, Rome, Italy

    G. Benfatto

Authors
  1. C. Chandre
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  2. H. R. Jauslin
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  3. G. Benfatto
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Chandre, C., Jauslin, H.R. & Benfatto, G. An Approximate KAM-Renormalization-Group Scheme for Hamiltonian Systems. Journal of Statistical Physics 94, 241–251 (1999). https://doi.org/10.1023/A:1004519514702

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