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Borel Summability and Lindstedt Series

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Abstract

Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the strength of the perturbation. Such series may be, sometimes, summed via suitable sum rules defining C ∞ functions of the perturbation strength: here we find sufficient conditions for the Borel summability of their sums in the case of two-dimensional rotation vectors with Diophantine exponent τ =1 (e.g. with ratio of the two independent frequencies equal to the golden mean).

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, Ohio, 43210, USA

    O. Costin

  2. Dipartimento di Fisica, Università di Roma “La Sapienza”, Roma, I-00185, Italy

    G. Gallavotti

  3. Dipartimento di Matematica, Università di Roma Tre, Roma, I-00146, Italy

    G. Gentile

  4. Department of Physics, Princeton University, Princeton, New Jersey, 08544, USA

    A. Giuliani

Authors
  1. O. Costin
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  2. G. Gallavotti
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  3. G. Gentile
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  4. A. Giuliani
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Corresponding author

Correspondence to A. Giuliani.

Additional information

Communicated by A. Kupiainen

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Costin, O., Gallavotti, G., Gentile, G. et al. Borel Summability and Lindstedt Series. Commun. Math. Phys. 269, 175–193 (2007). https://doi.org/10.1007/s00220-006-0079-0

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  • DOI: https://doi.org/10.1007/s00220-006-0079-0

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