Sur un aspect numérique de la dimension fractale d'un attracteur chaotique

N. Akroune

In this work, we apply a modified box-counting method to estimate the fractal dimension $D$ of a chaotic attractor $E$ generated by a two-dimensional mapping. The obtained numerical results show that the computed value of the capacity dimension $(d_{cap})$ tends to a limit value when the number of points $(n=card(E))$ increases. The function which fits the points $(n,D(n))$ has a sigmoidal form, and its expression characterizes the capacity dimension of chaotic attractors related to different discrete dynamical systems.