直角三角形台球系统的符号动力学分析

Symbolic Dynamic Analysis of Right Triangular Billiard

文章建立直角三角形台球系统的符号动力学描述。通过把直角三角形台球桌内台球运动的方程化简成二维分片映射,得到了相平面上的分割线,从而正、逆映射的分叶线分别被赋予了正、逆向单边无穷符号序列,建立了相空间轨道和符号序列空间的对应。引入度规后,符号空间转化为符号平面,并在符号平面上定义了基本禁止区,初步分析了系统的动力学行为。

The symbolic dynamics or the right triangular billiard is studied in this paper. A two-dimensional piecewise map is constructed to describe the billiard dynamics. The map has two partition lines which appear as straight lines. The phase space is thus foliated flowing the forward and backward maps in a simple manner. With the help of the basic forbidden zone on the symbolic plane, the dynamics of the system is studied primarily.