标题： 哈密顿混沌的哈密顿结构 显示英文标题

标题： Hamiltonian structure of Hamiltonian chaos

摘要： 从运动学的角度来看，哈密顿混沌的几何信息由（非）稳定方向给出，而动力学信息则由李雅普诺夫指数给出。 有限时间李雅普诺夫指数在物理学中具有特殊的重要性。 有限时间李雅普诺夫指数的空间变化及其相关的（非）稳定方向之间存在联系。 发现它们都由一个新的与原哈密顿系统自由度相同的哈密顿量决定。 这个新的哈密顿量定义了一个具有典型混沌轨迹的流场。 相流场的方向和大小给出了原始哈密顿系统的（非）稳定方向和有限时间李雅普诺夫指数。 我们的分析基于一个$1{1\over 2}$自由度的哈密顿系统。 显示英文摘要

摘要： From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are found to be determined by a new hamiltonian of same number of degrees of freedom as the original one. This new hamiltonian defines a flow field with characteristically chaotic trajectories. The direction and the magnitude of the phase flow field give the (un)stable direction and the finite time Lyapunov exponent of the original hamiltonian. Our analysis was based on a $1{1\over 2}$ degree of freedom hamiltonian system.