Penne V., Saussol B., Vaienti S. Fractal and statistical characteristics of recurrence times (68K, LATeX 2e) ABSTRACT. In this paper we introduce and discuss two proprieties related to recurrences in dynamical systems. The first gives the asymptotic law for the return time in a neighborhood, while the second gives a topological index of fractal type to characterize the system or some regions of the system.