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The Steep Nekhoroshev’s Theorem

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Abstract

Revising Nekhoroshev’s geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev’s theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be \({1/(2n\alpha_1\cdots\alpha_{n-2}}\)) (\({\alpha_i}\)’s being Nekhoroshev’s steepness indices and \({n \ge 3}\) the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    M. Guzzo & G. Benettin

  2. Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Largo San L. Murialdo 1, 00146, Rome, Italy

    L. Chierchia

Authors
  1. M. Guzzo
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  2. L. Chierchia
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  3. G. Benettin
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Correspondence to M. Guzzo.

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Communicated by K. Khanin

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Guzzo, M., Chierchia, L. & Benettin, G. The Steep Nekhoroshev’s Theorem. Commun. Math. Phys. 342, 569–601 (2016). https://doi.org/10.1007/s00220-015-2555-x

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  • DOI: https://doi.org/10.1007/s00220-015-2555-x

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