Chaotic behaviours of different time-scales in the trans-Neptunian space

The trans-Neptunian space is of great interest of dynamical studies with an inexhaustible number of intriguing problems to be solved. Its dynamical structure is shaped to a great extent by the different types of celestial mechanical resonances, such as mean-motion resonances (MMRs), secular resonances, and the Kozai resonance.

In a recent research, we carried out a large-scale survey of the trans-Neptunian objects (TNOs) by means of dynamical maps. We identified the most important MMRs and explored their dynamical role through the quantification of the chaotic diffusion and that of the stability times of the small bodies. The chaotic diffusion is of fundamental importance for its rate determines the long-term evolution of a given celestial system. To estimate the rate of the diffusion (that is, to compute the diffusion coefficients) in the case of more than 4100 TNOs, we initiated the use of the Shannon entropy. This latter quantity allows, on the one hand, to measure the extent of unstable regions in the phase space (and thus serves as an indicator of chaos), and also enables the direct measurement of the diffusion coefficients. The characteristic times of stability - in the case of normal diffusion - are then achieved by taking the inverse of the diffusion coefficients. In the knowledge of the chaotic diffusion and stability times for as large a TNO sample as the one indicated above, the overall structure of the trans-Neptunian space can be mapped, along with the specification of dynamical classes or the update of the existing ones.