Self-similar trajectories in multi-input systems

Self-similar trajectories play an important role in deterministic feedback control systems that possess a symmetry group of Fuller type. We consider self-similar trajectories in multi-input systems and the linear part of the associated Poincaré maps in orbit space with respect to the symmetry group. We show that Fuller groups contract the symplectic structure of the system’s phase space and derive some properties of the spectrum and the eigenvectors of the Poincaré map.