  The S-matrix in the static limit of a dispersion relation has a finite order
N and is a matrix of meromorfic functions of energy in the complex plane with
cuts. In the elastic case it reduces to N functions connected by the crossing
symmetry matrix A. The problem of analytical continuation of S - matrix from
the physical sheet to unphysical ones can be treated as a nonlinear system of
difference equations. It is shown that a global analisis of this system can be
carried out effectively in projective spaces. Some applications of the method
used are considered.
