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

Abstract

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