Consider an n-degrees-of-freedom real-analytic mechanical system with potential $\epsilon f = \epsilon f(x)$, x being a n-dimensional angle variable. Then, for ‘‘general’’ potentials f ’s and $\epsilon$ small enough, the Liouville measure of the complementary of invariant tori is smaller than $\epsilon |\ln \epsilon|^a (for a suitable a > 0).
Biasco, L., Chierchia, L. (2015). On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. CLASSE DI SCIENZE FISICHE, MATEMATICHE E NATURALI. RENDICONTI LINCEI. SUPPLEMENTO, 26(4), 423-432 [10.4171/RLM/713].
On the measure of Lagrangian invariant tori in nearly-integrable mechanical systems
BIASCO, LUCA;CHIERCHIA, Luigi
2015-01-01
Abstract
Consider an n-degrees-of-freedom real-analytic mechanical system with potential $\epsilon f = \epsilon f(x)$, x being a n-dimensional angle variable. Then, for ‘‘general’’ potentials f ’s and $\epsilon$ small enough, the Liouville measure of the complementary of invariant tori is smaller than $\epsilon |\ln \epsilon|^a (for a suitable a > 0).| File | Dimensione | Formato | |
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