A dynamical survey of the trans-Neptunian region − II. On the nature of chaotic diffusion

Abstract

ABSTRACT On long enough time-scales, chaotic diffusion has the potential to significantly alter the appearance of a dynamical system. The Solar system is no exception: diffusive processes take part in the transportation of small bodies and provide dynamical pathways even for the distant trans-Neptunian objects to reach the inner Solar system. In this letter, we carry out a thorough investigation of the nature of chaotic diffusion. We analyse the temporal evolution of the mean squared displacement of 10 000 ensembles of test particles and quantify in each case the diffusion exponent (enabling the classification between normal, sub-, and superdiffusion), the generalized diffusion coefficient, and a characteristic diffusion time-scale, too. This latter quantity is compared with an entropy-based time-scale, and the two approaches are studied in light of direct computations as well. Our results are given in the context of two-dimensional maps, thereby facilitating the understanding of the relationship between the typical phase space structures and the properties of chaotic diffusion.