Interpolated mapping system identification as a numerical algorithm

A new method for nonlinear system identification, based on the technique of Interpolated Mapping, is formulated. The input to the procedure is a map, taking initial conditions on a regular grid to their images after a fixed time step. It is assumed that the underlying dynamics evolves in continuous time. The given map is then replaced by a cascade of maps with progressively smaller time steps. When the time step becomes sufficiently small, the vector field underlying the map is estimated by way of difference quotients.