Consider an -degrees-of-freedom real-analytic mechanical system with potential , being a -dimensional angle variable. Then, for ‘‘general’’ potentials ’s and small enough, the Liouville measure of the complementary of invariant tori is smaller than (for a suitable ).
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. 423–432DOI 10.4171/RLM/713