Emmanouilidou A, Jung C
Center for Nonlinear Science, School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332-0430, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016219. doi: 10.1103/PhysRevE.73.016219. Epub 2006 Jan 30.
In this paper, we demonstrate a recent procedure for the construction of a symbolic dynamics for open systems by applying it to a model potential, the driven inverted Gaussian, which has proven very useful in describing laser-atom interaction. The symbolic dynamics and the corresponding partition of the Poincaré map are natural from the point of view of an asymptotic observer since the resulting branching tree coincides with the one extracted from the scattering functions. In general, the whole procedure is approximate because it only describes the globally unstable part of the chaotic invariant set, that is, the part that can be seen by an asymptotic observer in scattering data. It ignores Kolmogorov-Arnold-Moser islands and their fractal surroundings.
在本文中，我们展示了一种用于构建开放系统符号动力学的最新方法，即将其应用于一个模型势——驱动倒高斯势，该势在描述激光 - 原子相互作用方面已被证明非常有用。从渐近观察者的角度来看，符号动力学以及庞加莱映射的相应划分是自然的，因为所得的分支树与从散射函数中提取的分支树一致。一般来说，整个过程是近似的，因为它只描述了混沌不变集的全局不稳定部分，即渐近观察者在散射数据中可以看到的部分。它忽略了柯尔莫哥洛夫 - 阿诺尔德 - 莫泽岛及其分形周围环境。
