标题： q-环面上的能量局域化，长期稳定性以及FPU复发的解释 显示英文标题

标题： Energy localization on q-tori, long term stability and the interpretation of FPU recurrences

摘要： 我们关注近年来为解释所谓的FPU悖论提出的两种方法，即：在低能情况下，能量局域化现象持续存在于Fermi-Pasta-Ulam非线性晶格的“低-q”傅里叶模中，阻止了所有模之间的均分。 在第一种方法中，初始激发了频谱的低频部分，导致形成“自然包络”，表现出指数稳定性；而在第二种方法中，则强调“q-呼吸子”的存在，即晶格线性模的周期延拓，在傅里叶空间中呈指数局域化。 根据后一种思想，我们在本文中引入了“q-环面”的概念，表示低维环面上的指数局域解，并利用它们的稳定性特性来调和这两种方法，提供对FPU悖论更完整的解释。 显示英文摘要

摘要： We focus on two approaches that have been proposed in recent years for the explanation of the so-called FPU paradox, i.e. the persistence of energy localization in the `low-q' Fourier modes of Fermi-Pasta-Ulam nonlinear lattices, preventing equipartition among all modes at low energies. In the first approach, a low-frequency fraction of the spectrum is initially excited leading to the formation of `natural packets' exhibiting exponential stability, while in the second, emphasis is placed on the existence of `q-breathers', i.e periodic continuations of the linear modes of the lattice, which are exponentially localized in Fourier space. Following ideas of the latter, we introduce in this paper the concept of `q-tori' representing exponentially localized solutions on low-dimensional tori and use their stability properties to reconcile these two approaches and provide a more complete explanation of the FPU paradox.