Multidimensional dynamic processes studied by symbolic analysis in velocity-curvature space

A new computer-aided method for the symbolic analysis of discrete mappings and sequences is proposed that is based on a finite discretization of the velocity-curvature space. A minimum alphabet is introduced in a natural way. A number of initial analytical measures are defined that make it possible to study the dynamics structure of multidimensional discrete mappings, continuous systems, and dynamic processes. The proposed analytical method is tested by applying it to a logistic oscillator in the domain to the right of the period-doubling limit point, and the method is shown to be informative. It is revealed that the oscillation structure of the logistic map is highly asymmetric. The critical parameter values are found at which the geometric structure of the map trajectories changes qualitatively.