论文标题
多尺度曲线的kaM定理
KAM Theorems for Multi-scale Torus
论文作者
论文摘要
在本文中，从物理直觉的角度来看，我们引入了一个带有多尺度旋转的哈密顿系统，其中描述了许多系统，例如，具有快速旋转的强制摆，弱耦合的$ n $ soscillators具有quasiperiodic force等。我们研究了这个哈密顿系统不变的托里的持久性，并建立了一些KAM类型的结果，包括同工型类型。结果，我们可以证明Boltzmann的真诚假说对于这个哈密顿制度也不正确。
In present paper, from the viewpoint of physical intuition we introduce a Hamiltonian system with multiscale rotation, which describes many systems, for example, the forced pendulum with fast rotation, weakly coupled $N$-oscillators with quasiperiodic force and so on. We study the persistence of invariant tori for this Hamiltonian system, and establish some KAM type results including the isoenergetic type. As consequences, we can show that Boltzmann's ergodicity hypothesis is also not true for this Hamiltonian system.
