JournalsrlmVol. 26, No. 4pp. 423–432

On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems

  • Luca Biasco

    Università degli studi Roma Tre, Italy
  • Luigi Chierchia

    Università degli Studi Roma Tre, Italy
On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems cover
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Abstract

Consider an nn-degrees-of-freedom real-analytic mechanical system with potential ϵf=ϵf(x)\epsilon f = \epsilon f (x), xx being a nn-dimensional angle variable. Then, for ‘‘general’’ potentials ff’s and ϵ\epsilon small enough, the Liouville measure of the complementary of invariant tori is smaller than ϵlnϵa\epsilon |\mathrm {ln} \epsilon |^a (for a suitable a>0a > 0).

Cite this article

Luca Biasco, Luigi Chierchia, On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 4, pp. 423–432

DOI 10.4171/RLM/713