On persistence of invariant tori and a theorem by Nekhoroshev

2001/11/30 by Dario Bambusi, Giuseppe Gaeta
Physics and Astronomy · Mathematics · #math-ph #math.DS #math.MP

paper · pdf

published as Math. Phyl. El. J. 8 (2002), 1-13 · 13 pages, no figures

arxiv created 2002/03/09 · arxiv updated 2009/11/30

Abstract

We give a proof of a theorem by N.N. Nekhoroshev concerning Hamiltonian systems with n degrees of freedom and s integrals of motion in involution, where 1 ≤ s ≤ n. Such a theorem ensures persistence of s-dimensional invariant tori under suitable nondegeneracy conditions generalizing Poincaré's condition on the Floquet multipliers.

Related

• The Poincare'-Nekhoroshev map
• Invariant tori for commuting Hamiltonian PDEs
• Kolmogorov's Theorem for Low-Dimensional Invariant Tori of Hamiltonian\n Systems
• Positive measure of KAM tori for finitely differentiable Hamiltonians
• Persistence of lower dimensional invariant tori on sub-manifolds in Hamiltonian systems