On some systems of difference equations

摘要

In this note we show that the following systems of difference equationsun+1=vn1+vn,vn+1=un1+un,un+1=vn1+un,vn+1=un1+vn,un+1=un1+vn,vn+1=vn1+unwith n∈N0 and complex initial values u0 and v0, are solvable explicitly by means of Riccati equations, and based on the formulae for the general solutions we present the behaviour of their solutions as n→∞. While the result is natural for the first system, it is a bit surprising for the other two systems.