从不稳定周期轨道到哈密顿格点中的李雅普诺夫指数和宏观变量：周期轨道依赖性
From a unstable periodic orbit to Lyapunov exponent and macroscopic variable in a Hamiltonian lattice : Periodic orbit dependencies
摘要：
研究了多自由度Hamilton系统中相空间中的周期轨道与最大李雅普诺夫指数和宏观变量的期望值之间的联系。本文所用的模型是离散的非线性薛定谔方程。利用基于周期轨道调制估计的方法，我们预测了宏观变量的最大李雅普诺夫指数和期望值。我们表明，（i）预测的最大李雅普诺夫指数一般取决于我们采用的周期轨道，和（ii）预测的宏观变量的期望值不依赖于周期轨道至少在高能量制度。此外，考虑这些依赖关系的物理意义。
英文摘要：
We study which and how a periodic orbit in phase space links to both the largest Lyapunov exponent and the expectation values of macroscopic variables in a Hamiltonian system with many degrees of freedom. The model which we use in this paper is the discrete nonlinear Schrödinger equation. Using a method based on the modulational estimate of a periodic orbit, we predict the largest Lyapunov exponent and the expectation value of a macroscopic variable. We show that (i) the predicted largest Lyapunov exponent generally depends on the periodic orbit which we employ, and (ii) the predicted expectation value of the macroscopic variable does not depend on the periodic orbit at least in a high energy regime. In addition, the physical meanings of these dependencies are considered.
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