Detection of separatrices and chaotic seas based on orbit amplitudes

Abstract

The Maximum Eccentricity Method (MEM) 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.

Under review at Celestial Mechanics and Dynamical Astronomy. 8 Figures, 59 references, 17 pages. Comments and feedback welcome

References in corpus (14)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• Six transiting planets and a chain of Laplace resonances in TOI-178
• TOI-1338: TESS' First Transiting Circumbinary Planet
• Lagrangian Descriptors for Two Dimensional, Area Preserving, Autonomous and Nonautonomous Maps
• A comparison of different indicators of chaos based on the deviation vectors. Application to symplectic mappings
• Dynamical cartography of Earth satellite orbits
• Chaos detection tools: application to a self-consistent triaxial model
• TRAPPIST-1: Dynamical analysis of the transit-timing variations and origin of the resonant chain
• An integrable model for first-order three-planet mean motion resonances
• A general stability-driven approach for the refinement of multi-planet systems
• Modeling Radial Velocity Data of Resonant Planets to Infer Migration Histories
• Laplace-like resonances with tidal effects
• Finding regions of bounded motion in binary asteroid environment using Lagrangian descriptors
• Web of resonances and possible path of evolution of the small Uranian satellites

Cited by in corpus (3)

• Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
• Uncontrolled geostationary satellites: mapping periodic transitions to chaos with Lagrangian Descriptors
• TESS and HARPS-N unveil two planets transiting TOI-1453. A super-Earth and one of the lowest mass sub-Neptunes