Stability analysis of planetary systems via second-order Renyi entropy

The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data are continuously growing and the precision allows us to obtain accurate planetary orbits, the canonical stability analysis still requires N-body simulations and phase space trajectory investigations. We propose a method for stability analysis of planetary motion based on the generalized Renyi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem are used as the basis of a phase space reconstruction procedure. Then, Poincare's recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the Renyi entropy. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods, and it requires only a few tens of thousands of orbital period integration time.

Automated summary

The long-term dynamical evolution plays a crucial role in planetary research. This paper proposes a stability analysis method based on the generalized Renyi entropy, which is obtained from scalar measurements. By reconstructing the phase space using radial velocity data, Poincare's recurrence theorem helps to obtain the Renyi entropy. The results show that the entropy-based stability analysis is consistent with other chaos detection methods and only requires a relatively short integration time.