Drótos G, Jung C, Tél T
Institute of Theoretical Physics, Eötvös University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056210. doi: 10.1103/PhysRevE.86.056210. Epub 2012 Nov 16.
We demonstrate how the area of the enveloping surface of the scattering singularities in a three-degrees-of-freedom (3-dof) system depends on a perturbation parameter controlling the distance from a reducible case. This dependence is monotonic and approximately linear. Therefore it serves as a measure for this distance, which can be extracted from an investigation of the fractal structure. These features are a consequence of the dynamics being governed by normally hyperbolic invariant manifolds. We conclude that typical n-dof chaotic scattering exhibits either structures developing out of a stack of chaotic structures of 2-dof type or hardly any chaotic effects.
我们展示了在一个三自由度（3-dof）系统中，散射奇点的包络面面积如何取决于控制与可约情形距离的微扰参数。这种依赖关系是单调的且近似线性的。因此，它可作为该距离的一种度量，可从分形结构的研究中提取出来。这些特征是由正常双曲不变流形支配动力学的结果。我们得出结论，典型的n自由度混沌散射要么呈现出由二维自由度类型的混沌结构堆叠发展而来的结构，要么几乎没有任何混沌效应。
