一类有理离散系统的周期解

The Periodic Solutions of a Class of Rational Dscrete Systems

利用射影几何中常用的齐次坐标把Xn+1=(Axn+Bxn-1+C)/(pxn-1+q)用线性形式表出,利用线性代数的理论,得到了方程有最小正周期的一个充要条件,作为应用和例子,给出了最小正周期m=1,2,3,4时的一般表达式.

In this paper the difference equation Xn＋1=（Axn＋Bxn-1＋C）/（pxn-1＋q） is expressed as a linear form by using the homogeneous coordinates in projective geometry. From the theory of linear algebra a sufficient and necessary condition is given for the equation to be with the least periodic solution. As an application ,example a general expression is obtained for the equation with the least period m = 1,2,3 and 4.