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

Autor:	Biasco, L., Chierchia, L.
Rok vydání:	2015
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	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 $a>0$).
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1503.08145 Zobrazit plný text záznamu View this record from Arxiv