Matrix Hermite–Padé problem and dynamical systems

The solution of a discrete dynamical system is studied. To do so spectral properties of the band operator, with intermediate zero diagonals, are investigated. The method of genetic sums for the moments of the Weyl function is used to find the continued fraction associated to this Weyl function. It is possible to follow the inverse spectral method to solve dynamical systems defined by a Lax pair.