论文标题
迪克森系统中没有混乱
No Chaos in Dixon's System
论文作者
论文摘要
如果其两个参数在某个域中具有其值，则通常将所谓的Dixon系统作为二维（连续）动力学系统的示例。首先，我们提供了严格的证据，证明迪克森系统中没有混乱。然后，我们对系统进行完整的分叉分析，表明参数空间可以分解为十六个不同区域，在该区域中，系统在质量上表现出相同的行为。特别是，我们证明在某些地区存在两个具有无限许多同质轨道轨道的椭圆形扇区。
The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behaviour, if its two parameters take their value in a certain domain. We provide first a rigorous proof that there is no chaos in Dixon's system. Then we perform a complete bifurcation analysis of the system showing that the parameter space can be decomposed into sixteen different regions in each of which the system exhibits qualitatively the same behaviour. In particular, we prove that in some regions two elliptic sectors with infinitely many homoclinic orbits exist.
