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arXiv · 1503.08145

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

L. Biasco·L. Chierchia
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Abstract

Consider a real--analytic nearly--integrable mechanical system with potential $f$, namely, a Hamiltonian system, having a real-analytic Hamiltonian $$ H(y,x)=\frac12 | y |^2 +\e f(x)\ , $$ $y,x$ being $n$--dimensional standard action--angle variables (and $|\cdot|$ the Euclidean norm). Then, for "general" potentials $f$'s and $\e$ small enough, the Liouville measure of the complementary of invariant tori is smaller than $\e|\ln \e|^a$ (for a suitable $a>0$).

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L. Biasco, L. Chierchia. 2015-03-27. On the measure of Lagrangian invariant tori in nearly--integrable mechanical systems (draft). https://arxiv.org/abs/1503.08145

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