  The theory of recurrence relations of linear multi-component and
multi-parameter systems on the basis of the canonical transformations theory of
the dynamical systems' sets is constructed. The parameters of the grating's
knots are defined from the condition of the invariance of the model under
shifts along the grating. The connection with a zero curvature representation
for models on the grating is installed. The examples of two- and
three-parameter systems described by the hypergeometric functions
M(\alpha,\beta,t) and M(\alpha,\beta,\xi,t) are considered in details. The
canonical recurrence relations increasing and decreasing parameters
{\alpha,\beta,\xi} for solutions of the corresponding equations are
constructed.
