Analytic solutions of systems of functional equations (Q805939)

The paper deals with a system of difference equations \((*)\quad X_{n+1}=A_ 1X_ n+\mu F_ 1(X_ n,Y_ n,\mu),\) \(Y_{n+1}=A_ 2Y_ n+\mu F_ 2(X_ n,Y_ n,\mu),\) where \(X_ n\in {\mathbb{C}}^ q\), \(Y_ n\in {\mathbb{C}}^ p\), \(\mu >0\), \(F_ i\), \(i=1,2\), are analytic functions of the first two variables, and \(A_ i\), \(i=1,2\), are square matrices. Under some additional assumptions the author proves a theorem on the structure of solutions of (*). He solves also functional equations for analytic functions, which define integral manifolds of solutions of (*).