Localization of Arnold tongues of discrete dynamical systems

Abstract

The work is devoted to the exposition of the method of localizing the Arnold tongues for finite-dimensional dynamical systems with a discrete time which are the sets corresponding to rationally synchronized relations between the system's parameters. Such sets correspond to regions of parameter values for which the system has cycles of certain periods. The method allows us to obtain an approximate representation of the Arnold tongues, to study their properties in the major and minor resonances.