TY - JOUR
T1 - Detection of separatrices and chaotic seas based on orbit amplitudes
AU - Daquin, Jerome
AU - Charalambous, Carolina
N1 - Funding Information:
J. D. is a postdoctoral researcher of the “Fonds de la Recherche Scientifique” - FNRS. C.C. acknowledges FNRS Grant No. F.4523.20 (DYNAMITE MIS-project). We thank both anonymous reviewers for their report that helped us improve our manuscript. We acknowledge discussions with Elisa Maria Alessi, Ana Maria Mancho, Guillermo García-Sánchez and Timoteo Carletti.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/5/18
Y1 - 2023/5/18
N2 - 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.
AB - 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.
KW - Dynamical indicator
KW - Maximum eccentricity method
KW - Mean-motion resonances
KW - Planetary systems
KW - Stability maps
UR - http://www.scopus.com/inward/record.url?scp=85160099514&partnerID=8YFLogxK
U2 - 10.1007/s10569-023-10143-6
DO - 10.1007/s10569-023-10143-6
M3 - Article
SN - 0923-2958
VL - 135
JO - Celestial Mechanics & Dynamical Astronomy
JF - Celestial Mechanics & Dynamical Astronomy
IS - 3
M1 - 31
ER -