Quantifying chaos using Lagrangian descriptors

Detection of separatrices and chaotic seas based on orbit amplitudes

“…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.…”