Stability analysis of planetary systems via second-order Rényi entropy

Abstract

The long-term dynamical evolution is a crucial point in recent planetary research. Although the amount of observational data is 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 Rényi entropy obtained from a scalar measurement. The radial velocity data of the central body in the gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincaré's recurrence theorem contributes to finding a natural partitioning in the reconstructed phase space to obtain the Rényi 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.

7 pages, 7 figures, accepted for publication in MNRAS

References in corpus (7)

• Recurrence time analysis, long-term correlations, and extreme events
• On the Dynamical Stability of the Solar System
• Extended Recurrence Plot Analysis and its Application to ERP Data
• Chirikov Diffusion in the Asteroidal Three-Body Resonance (5,-2,-2)
• Early Warning Signals Indicate a Critical Transition in Betelgeuse
• Shannon Entropy Applied to the Planar Restricted Three-Body Problem
• Stability of exoplanetary systems retrieved from scalar time series