Periodicity in the asymmetrical quartic map

We report the dynamics of the asymmetrical quartic map, a one-dimensional discrete-time system constructed adding one linear and one cubic term to the biquadratic form of the quartic map. Here, we analyze the stability of periodic orbits in complex structures living in the parameter space for the map. To this end, we developed a new methodology to investigate the inner structure and organization of periodicity domains, applying the new technique to construct reliable high-resolution phase diagrams. Our analysis allows us to follow all metamorphoses of the complex structures in new classes of periodic objects while the parameters of the map change.