Detection of separatrices and chaotic seas based on orbit amplitudes

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Résumé

The maximum eccentricity method (MEM, (Dvorak et al. in Astron Astrophys 426(2):L37–L40, 2004)) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper leverages on the MEM to introduce a sharp detector of separatrices and chaotic seas. After introducing the MEM analogue for nearly-integrable action-angle Hamiltonians, i.e., diameters, we use low-dimensional dynamical systems with multi-resonant modes and junctions, supporting chaotic motions, to recognise the drivers of the diameter metric. Once this is appreciated, we present a second-derivative-based index measuring the regularity of this application. This quantity turns to be a sensitive and robust indicator to detect separatrices, resonant webs and chaotic seas. We discuss practical applications of this framework in the context of N-body simulations for the planetary case affected by mean-motion resonances, and demonstrate the ability of the index to distinguish minute structures of the phase space, otherwise undetected with the original MEM.

langue originaleAnglais
Numéro d'article31
journalCelestial Mechanics & Dynamical Astronomy
Volume135
Numéro de publication3
Les DOIs
Etat de la publicationPublié - 18 mai 2023

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