三自由度以上混沌散射的混沌集和混沌散射截面
The chaotic set and the cross section for chaotic scattering beyond in 3 degrees of freedom
摘要：
本文将混沌散射与三个自由度，其中之一是开放的，其他两个是封闭的，作为第一步，更一般的理解混沌散射在更高的维度。尽管有很强的限制，它打破了任何二维时间无关散射问题中隐含的基本简单性。通过打破连续对称性引入第三自由度，我们首先探讨了同宿/异宿纠缠的拓扑结构和散射函数的结构。然后，我们工作的影响，这些结构的双微分截面。在截面中最突出的结构是彩虹奇点。它们形成一个分形图案，反映了混沌不变集的分形结构。这允许从不变集确定截面中的结构，并且相反地，从截面获得关于不变集的拓扑的信息。后者是混沌系统的逆散射问题的贡献。
英文摘要：
This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step toward a more general understanding of chaotic scattering in higher dimensions. Despite of the strong restrictions it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern which reflects the fractal structure of the chaotic invariant set. This allows to determine structures in the cross section from the invariant set and conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
