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

Abstract

This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this method requires only the knowledge of orbits on finite time windows and is free of the computation of the tangent vector dynamics (i.e., variational equations are not needed). To demonstrate its ability in visualising different dynamical behaviors, in particular for highlighting chaotic regions, several stability maps of classical systems, obtained with different phase space methods, are reproduced. The benchmark examples are rooted in discrete and continuous nearly-integrable dynamical systems, with prominent features played by resonances. These include the Chirikov standard map, higher dimensional symplectic and volume preserving maps, fundamental models of resonances, and a 3 degrees-of-freedom nearly-integrable Hamiltonian system with a dense web of resonances. The indicator thus appears to be relevant for understanding phase space transport mediated by resonances in nearly-integrable system, as ubiquitous in celestial mechanics or astrodynamics.

arXiv commentv3: Accepted for publication in Physica D. Minor modifications. 4 references added. 22 pages, 64 references. v2: Slight modification of the title. 15 references added, 2 Figures added. v1: 22 pages, 9 figures, 60 references. Comments and feedback are welcome

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Cited by in corpus (8)

• Quantifying chaos using Lagrangian descriptors
• Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map
• Improved detection of chaos with Lagrangian descriptors using differential algebra
• Classical dynamics and semiclassical analysis of excitons in cuprous oxide
• Revisiting the Toda-Brumer-Duff criterion for order-chaos transition in dynamical systems
• Rydberg excitons in cuprous oxide: A two-particle system with classical chaos
• Advanced Techniques in Stability Analysis of Trans-Neptunian Objects
• Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach