Riemann surfaces of some static dispersion models and projective spaces

We show that the analytic continuation of the S-matrix elements, which are meromorphic functions of the energy omega in the complex plane wit h the cuts (-infinity, - 1] and [+ 1, +infinity), from the physical sheet to nonphysical ones results in a system of nonlinear difference equations. A global analysis of this system is performed in the projective spaces P-N and PN+1. We discuss the connection between the spaces P-N and PN+1 and obtain some particular solutions of the initial system.