Rypina I I, Brown M G, Beron-Vera F J, Koçak H, Olascoaga M J, Udovydchenkov I A
RSMAS/AMP, University of Miami, 4600 Rickenbacker Causeway, Miami, Florida 33149, USA.
Phys Rev Lett. 2007 Mar 9;98(10):104102. doi: 10.1103/PhysRevLett.98.104102. Epub 2007 Mar 8.
Hamiltonian systems that locally violate the twist condition arise in many applications. Numerical simulations reveal that, when systems of this type are perturbed, the degenerate or nontwist tori are remarkably stable. This phenomenon, which we refer to as strong Kolmogorov-Arnold-Moser (KAM) stability, is shown to be linked to very small resonance widths near degenerate tori. Quantitative estimates of degenerate resonance widths are derived and bifurcations of degenerate resonances are described. Strong KAM stability leads to robust transport barriers, which are important in all of the many applications in which Hamilitonians with the nontwist property arise.
局部违反扭转条件的哈密顿系统出现在许多应用中。数值模拟表明，当这类系统受到扰动时，退化或非扭转环面非常稳定。我们将这种现象称为强柯尔莫哥洛夫 - 阿诺德 - 莫泽（KAM）稳定性，它被证明与退化环面附近非常小的共振宽度有关。推导了退化共振宽度的定量估计，并描述了退化共振的分岔。强KAM稳定性导致了鲁棒的输运障碍，这在出现具有非扭转性质哈密顿量的所有众多应用中都很重要。
