Lai YC, Grebogi C
Department of Mathematics, Department of Electrical Engineering, and Department of Physics, Center for Systems Science and Engineering Research, Arizona State University, Tempe, Arizona 85287-1804, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Nov;62(5 Pt A):6421-8. doi: 10.1103/physreve.62.6421.
We investigate Hamiltonian chaotic scattering in physically realistic three-dimensional potentials. We find that the basin topology of the scattering dynamics can undergo a metamorphosis from being totally disconnected to being connected as a system parameter, such as the particle energy, is varied through a critical value. The dynamical origin of the metamorphosis is investigated, and the topological change in the scattering basin is explained in terms of the change in the structure of the invariant set of nonescaping orbits. A dynamical consequence of this metamorphosis is that the fractal dimension of the chaotic set responsible for the chaotic scattering changes its behavior characteristically at the metamorphosis. This topological metamorphosis has no correspondence in two-degree-of-freedom open Hamiltonian systems.
我们研究了物理上现实的三维势中的哈密顿混沌散射。我们发现，随着诸如粒子能量等系统参数通过一个临界值变化时，散射动力学的相空间拓扑结构可以经历从完全不连通到连通的转变。我们研究了这种转变的动力学起源，并根据非逃逸轨道不变集结构的变化来解释散射相空间的拓扑变化。这种转变的一个动力学结果是，负责混沌散射的混沌集的分形维数在转变时其行为会发生特征性变化。这种拓扑转变在两自由度开放哈密顿系统中不存在对应情况。
