Entropy based stability analysis of planetary systems retrieved from scalar time series

Kovács Tamás, Kővári Emese, Forgács-Dajka Emese (2022.01.01 - 2022.03.30)
Eötvös Loránd University, Center for Astrophysics and Space Science

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 planet 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 gravitational three-body problem is used as the basis of a phase space reconstruction procedure. Then, Poincaré's recurrence theorem contributes to find a natural partitioning in the reconstructed phase space to obtain the Rényi entropy. High performance computing of phase space reconstruction and matrix manipulations allows us to investigate large data sets and long time series. It turns out that the entropy-based stability analysis is in good agreement with other chaos detection methods.

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