H-rank as a Control Tool for Discrete Dynamical Systems

The convergence to Arnold tongues is studied using computational techniques based on ranks of Hankel matrices (H-ranks). The ranks of Hankel matrices carry important physical information about transient processes taking place in discrete nonlinear iterative maps. We will show that the measurements of the convergence rate to Arlond tongues can reveal important physical information on the properties of the iterative system. Moreover, such enriched representation of Arnold tongues produces aesthetically beautiful pictures.