Dynamical Properties of the Composed Logistic-Gauss Map

In this paper, we study the Logistic-Gauss map. Such mapping presents cyclic curves inits parameter space, leading to period addition structures. We obtain the parameter spaceby changing two control parameters, while the third control parameter remains constant.For each combination of control parameters, we find the respective Lyapunov exponent. Aspecific color palette is then used to highlight complex sets of periodicity (CSP). Whenchanging a control parameter, some regions containing CSP structures gradually deformuntil the appearance of regions with high stability. We also use the theory of extreme andsuperstable curves to understand the organization of the CSP structures in the parameterspace. Finally, we obtain the bifurcation diagrams and returns maps to interpret parameterspace properties.