TY - JOUR
T1 - Global dynamics visualisation from Lagrangian Descriptors
T2 - Applications to discrete and continuous systems
AU - Daquin, Jerome
AU - PEDENON-ORLANDUCCI, Remi
AU - Agaoglou, Makrina
AU - Garcia-Sanchez, Guillermo
AU - Mancho, Ana Maria
N1 - Funding Information:
The authors are very grateful to Víctor J. García-Garrido and Stephen Wiggins for bringing to their knowledge their recent Refs. [44,47] and useful comments and suggestions. J.D. acknowledges warmly discussions and feedback from Carolina Charalambous, Anne Lemaitre and Timoteo Carletti. J.D. is a postdoctoral researcher of the “Fonds de la Recherche Scientifique” - FNRS. M.A. acknowledges support from the grant CEX2019-000904-S and IJC2019-040168-I funded by: MCIN/AEI/ 10.13039/ 501100011033. A.M.M acknowledges support from grant PID2021-123348OB-I00 funded by MCIN/ AEI /10.13039/501100011033/ and by FEDER A way to make Europe.
Funding Information:
The authors are very grateful to Víctor J. García-Garrido and Stephen Wiggins for bringing to their knowledge their recent Refs. [44,47] and useful comments and suggestions. J. D. acknowledges warmly discussions and feedback from Carolina Charalambous, Anne Lemaitre and Timoteo Carletti. J. D. is a postdoctoral researcher of the “Fonds de la Recherche Scientifique” - FNRS. M. A. acknowledges support from the grant CEX2019-000904-S and IJC2019-040168-I funded by: MCIN/AEI/ 10.13039/ 501100011033. A.M. M acknowledges support from grant PID2021-123348OB-I00 funded by MCIN/ AEI /10.13039/501100011033/ and by FEDER A way to make Europe.
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/12/15
Y1 - 2022/12/15
N2 - 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 equationsare not needed). To demonstrate its ability in visualising different dynamical behaviours, 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 includethe 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 orastrodynamics.
AB - 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 equationsare not needed). To demonstrate its ability in visualising different dynamical behaviours, 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 includethe 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 orastrodynamics.
KW - Finite time chaos indicator
KW - Global dynamics
KW - Lagrangian Descriptor
KW - Phase space methods
UR - http://www.scopus.com/inward/record.url?scp=85139595338&partnerID=8YFLogxK
U2 - 10.1016/j.physd.2022.133520
DO - 10.1016/j.physd.2022.133520
M3 - Article
SN - 0167-2789
VL - 442
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
M1 - 133520
ER -