Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems

Daquin, Jérôme; Remi, Pedenon-Orlanducci; Agaoglou, Makrina; García-Sánchez, Guillermo; Mancho, Ana M.

doi:10.1016/j.physd.2022.133520

Cited by 9 publications

(3 citation statements)

References 47 publications

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“…Recently, two non-variational chaos indicators have been proposed in concert from the Mfunction by Daquin et al (2022) and Hillebrand et al (2022). The present paper follows closely the steps of Daquin et al (2022) by recognising the resemblance of the M -function with MEM like quantities used in orbital settings.…”

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confidence: 76%

“…LDs have been precious allies over the years for gaining dynamical understandings in a variety of contexts and range of fields, such as the detection of Lagrangian coherent structures in geophysical and oceanic flows (see e.g., Mendoza and Mancho, 2010;Curbelo et al, 2019a,b), but also and especially in the field of reaction dynamics in theoretical chemistry, allowing to recover stable and unstable manifolds of normally hyperbolic invariant manifolds (NHIM) in a non-perturbative approach (see e.g., Craven and Hernandez, 2015;Feldmaier et al, 2017;Junginger et al, 2017;Nagahata et al, 2021). Recently, two non-variational chaos indicators have been proposed in concert from the Mfunction by Daquin et al (2022) and Hillebrand et al (2022). The present paper follows closely the steps of Daquin et al (2022) by recognising the resemblance of the M -function with MEM like quantities used in orbital settings.…”

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confidence: 99%

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Detection of separatrices and chaotic seas based on orbit amplitudes

Daquin

Charalambous

2022

Preprint

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The Maximum Eccentricity Method (MEM, Dvorak et al, 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, \ie 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.

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confidence: 76%

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confidence: 99%

Detection of separatrices and chaotic seas based on orbit amplitudes

Daquin

Charalambous

2022

Preprint

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“…It should be mentioned that the introduction of the index   DD follows from recent developments on Lagrangian descriptors and arc-length of orbits (Daquin et al 2022). Regarding the computation method (central difference) about the second derivatives of the diameter, please refer to Daquin & Charalambous (2023) for more details.…”

Section: Dynamical Mapsmentioning

confidence: 99%

Dynamical Structures Associated with High-Order and Secondary Resonances in the Spin–Orbit Problem

Lei

2024

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In our solar system, spin–orbit resonances are common under Sun–planet, planet–satellite, and binary asteroid configurations. In this work, high-order and secondary spin–orbit resonances are investigated by taking numerical and analytical approaches. Poincaré sections as well as two types of dynamical maps are produced, showing that there are complicated structures in the phase space. To understand numerical structures, we adopt the theory of perturbative treatments to formulate resonant Hamiltonian for describing spin–orbit resonances. The results show that there is an excellent agreement between analytical and numerical structures. It is concluded that the main V-shape structure arising in the parameter space ( θ ̇ , α ) is sculpted by the synchronous primary resonance, those minute structures inside the V-shape region are dominated by secondary resonances and those structures outside the V-shape region are governed by high-order resonances. Finally, the analytical approach is applied to binary asteroid systems (65803) Didymos and (4383) Suruga to reveal their phase-space structures.

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