Dynamical realizations of finite Volterra series

In this paper we investigate the structure of minimal realizations of finite volterra series, within the class of nonlinear, analytic systems. The structure of Nilmanifolds described by A. Malcev is used to show that the natural state space of these realizations is a vector space. Additionally it is shown that minimal realizations of finite Volterra series can be viewed as cascades of linear subsystems with polynomic link maps. The dimensions of these subsystems do not depend on the minimal realization, and an algorithm is given to compute them from the kernels.