Detection of separatrices and chaotic seas based on orbit amplitudes
arXiv:2212.02200 · doi:10.1007/s10569-023-10143-6
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 -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.
arXiv commentUnder review at Celestial Mechanics and Dynamical Astronomy. 8 Figures, 59 references, 17 pages. Comments and feedback welcome
References in corpus (37)
- Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
- Defining and cataloging exoplanets: The exoplanet.eu database
- A seven-planet resonant chain in TRAPPIST-1
- Multiple-Planet Scattering and the Origin of Hot Jupiters
- Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems
- Geometrical properties of local dynamics in Hamiltonian systems: the Generalized Alignment Index (GALI) method
- Six transiting planets and a chain of Laplace resonances in TOI-178
- Distinguished trajectories in time dependent vector fields
- The hidden geometry of ocean flows
- Three Body Resonance Overlap in Closely Spaced Multiple Planet Systems
- TOI-1338: TESS' First Transiting Circumbinary Planet
- Extrasolar Trojan Planets close to Habitable Zones
- 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
- The Resonance Overlap and Hill Stability Criteria Revisited
- Planetary migration and the origin of the 2:1 and 3:2 (near)-resonant population of close-in exoplanets
- From order to chaos in Earth satellite orbits
- An Integrable Model for the Dynamics of Planetary Mean Motion Resonances
- Dynamical cartography of Earth satellite orbits
- Obtaining time-dependent multi-dimensional dividing surfaces using Lagrangian descriptors
- Resonance Capture and Dynamics of 3-Planet Systems
- Chaos detection tools: application to a self-consistent triaxial model
- Planetary and satellite three body mean motion resonances
- Chemical dynamics between wells across a time-dependent barrier: Self-similarity in the Lagrangian descriptor and reactive basins
- Natural highways for end-of-life solutions in the LEO region
- New Lagrangian diagnostics for characterizing fluid flow mixing
- TRAPPIST-1: Dynamical analysis of the transit-timing variations and origin of the resonant chain
- Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The Vortex Splitting at Upper Levels
- Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure
- 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
- Diffusion and Drift in Volume-Preserving Maps
- Drift and its mediation in terrestrial orbits
- 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