Emmanouilidou A, Jung C, Reichl L E
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 2):046207. doi: 10.1103/PhysRevE.68.046207. Epub 2003 Oct 27.
We study the classical electron scattering from a driven inverted Gaussian potential, an open system, in terms of its chaotic invariant set. This chaotic invariant set is described by a ternary horseshoe construction on an appropriate Poincaré surface of section. We find the development parameters that describe the hyperbolic component of the chaotic invariant set. In addition, we show that the hierarchical structure of the fractal set of singularities of the scattering functions is the same as the structure of the chaotic invariant set. Finally, we construct a symbolic encoding of the hierarchical structure of the set of singularities of the scattering functions and use concepts from the thermodynamical formalism to obtain one of the measures of chaos of the fractal set of singularities, the topological entropy.
我们从其混沌不变集的角度研究了受驱动的倒高斯势（一个开放系统）中的经典电子散射。这个混沌不变集是通过在适当的庞加莱截面面上的三元马蹄形构造来描述的。我们找到了描述混沌不变集双曲分量的发展参数。此外，我们表明散射函数奇点分形集的层次结构与混沌不变集的结构相同。最后，我们构建了散射函数奇点集层次结构的符号编码，并使用热力学形式论中的概念来获得奇点分形集混沌的一种度量，即拓扑熵。
