递推序列y_(n+1)=p+y_(n-1)/qy_n+y_(n-1)的周期解

Periodic Solutions of the Recursive Sequence y_(n+1)=p+y_(n-1)/qy_n+y_(n-1)

首先,利用射影几何中常用的齐次坐标把序列yn+1=p+yn-1qyn+yn-1用线性形式表出.然后利用线性代数的理论,得出了序列有最小正周期的一个充要条件.作为应用和例子,给出了m=1,2,3时序列的一般表达式.

Fist, the homogeneous coordinates of projective geometry is used to establish the linearization equation of the yn+1=p-yn-1qyn+yn-1. Second, a sufficient and necessary conditions is presented for yn+1=p-yn-1qyn+yn-1 periodic solutions. Last, the generality equations having periodic solutions with period one, two and three are established as application.