  A novel strategy to automated classification is introduced which exploits a
fully trained dynamical system to steer items belonging to different categories
toward distinct asymptotic attractors. These latter are incorporated into the
model by taking advantage of the spectral decomposition of the operator that
rules the linear evolution across the processing network. Non-linear terms act
for a transient and allow to disentangle the data supplied as initial condition
to the discrete dynamical system, shaping the boundaries of different
attractors. The network can be equipped with several memory kernels which can
be sequentially activated for serial datasets handling. Our novel approach to
classification, that we here term Recurrent Spectral Network (RSN), is
successfully challenged against a simple test-bed model, created for
illustrative purposes, as well as a standard dataset for image processing
training.
