论文标题
混沌图的Koopman操作员和相空间分区
Koopman Operator and Phase Space Partition of Chaotic Maps
论文作者
论文摘要
Koopman操作员描述了相位空间中可观测值的演变，该分析物可用于提取非线性系统的特征动力学特征。在这里，我们表明，可以根据操作员的混乱地图进行正确构建的特征函数进行有趣的符号分区。分区边界是这些本征函数的极值，通过在数值计算中包含更多基础函数来提高其准确性。该方案的有效性在众所周知的1-D和2-D图中得到了证明。将计算扩展到高维的非线性系统似乎没有障碍，这提供了一种剖析复杂动力学的可能方法。
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions based on properly constructed eigenfunctions of the operator for chaotic maps. The partition boundaries are the extrema of these eigenfunctions, the accuracy of which is improved by including more basis functions in the numerical computation. The validity of this scheme is demonstrated in well-known 1-d and 2-d maps. It seems no obstacle to extend the computation to nonlinear systems of high dimensions, which provides a possible way of dissecting complex dynamics.
