论文标题
哈密顿和可逆系统，具有不变的托里家族
Hamiltonian and reversible systems with smooth families of invariant tori
论文作者
论文摘要
对于N，D和相空间维度的各种值，我们构建了具有不变的N-tori的平滑D参数家族的哈密顿和可逆系统的简单示例。在哈密顿式的情况下，这些摩尔氏菌可以是各向同性，侧相或展（既不是各向同性的也不是共同体）。考虑了非紧凑和紧凑的相位空间的情况。特别是，对于任何不少于3的n和r^n中的任何矢量欧米茄，我们提供了一个具有自由度的分析性哈密顿系统的示例，并具有n级（甚至是独特的）不变的n个毛孔，其有条件地带有带有频率矢量emega的周期性运动（但这种torus是torus而不是lagrangian and lagrangian and symplectic形式）。在论文中首次给出了孤立的肉食不变的托里的示例。该论文还可以用作对哈密顿和可逆系统中不变性托里孤立性的介绍。
For various values of n, d, and the phase space dimension, we construct simple examples of Hamiltonian and reversible systems possessing smooth d-parameter families of invariant n-tori carrying conditionally periodic motions. In the Hamiltonian case, these tori can be isotropic, coisotropic, or atropic (neither isotropic nor coisotropic). The cases of non-compact and compact phase spaces are considered. In particular, for any N no less than 3 and any vector omega in R^N, we present an example of an analytic Hamiltonian system with N degrees of freedom and with an isolated (and even unique) invariant N-torus carrying conditionally periodic motions with frequency vector omega (but this torus is atropic rather than Lagrangian and the symplectic form is not exact). Examples of isolated atropic invariant tori carrying conditionally periodic motions are given in the paper for the first time. The paper can also be used as an introduction to the problem of the isolatedness of invariant tori in Hamiltonian and reversible systems.
