论文标题
2个复杂均匀选的系统的定性特性：与多边形台球的连接
Qualitative properties of systems of 2 complex homogeneous ODE's: a connection to polygonal billiards
论文作者
论文摘要
显示了具有实际系数的2个复合物，均质的多项式差分方程的轨道与多边形台球的轨道之间的对应关系。这种对应关系是一般的，从某种意义上说，它适用于指定类型的普通微分方程的一组开放系统。这允许从多边形台球理论（例如千古，周期性轨道的存在，缺乏指数差异，额外的保护定律的存在以及动力学中存在不连续性的存在以及对相应的差分方程的相应系统中存在）。它还表明，多边形台球已知的相当复杂，也参加了这些显然更简单的普通微分方程系统。
A correspondence between the orbits of a system of 2 complex, homogeneous, polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed. This correspondence is general, in the sense that it applies to an open set of systems of ordinary differential equations of the specified kind. This allows to transfer results well-known from the theory of polygonal billiards, such as ergodicity, the existence of periodic orbits, the absence of exponential divergence, the existence of additional conservation laws, and the presence of discontinuities in the dynamics, to the corresponding systems of ordinary differential equations. It also shows that the considerable intricacy known to exist for polygonal billiards, also attends these apparently simpler systems of ordinary differential equations.
