On the use of the MEGNO indicator with the global symplectic integrator

Research output: Book/Report/JournalOther report

Abstract

To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced [Libert et al., 2010], based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In the present contribution, we show how to compute efficiently the MEGNO indicator jointly with the GSI. Moreover, we discuss the choice of symplectic integrator, in fact we point out that a particular attention has to be paid to the structure of the Hamiltonian system associated to the variational equations. The performances of our method is illustrated through the study of the Arnold diffusion problem.
Original languageEnglish
Place of PublicationNamur
PublisherFUNDP. Namur center for complex systems
Volume1
Edition6
Publication statusPublished - 29 Nov 2010

Publication series

NamenaXys Technical Reports Series
PublisherUniversity of Namur
No.6
Volume1

Fingerprint

Symplectic Integrators
Variational Equation
Hamiltonian Systems
Symplectic Integration
Arnold Diffusion
Diffusion Problem
Equations of Motion
Orbit

Cite this

Hubaux, C., Libert, A-S., & Carletti, T. (2010). On the use of the MEGNO indicator with the global symplectic integrator. (6 ed.) (naXys Technical Reports Series; Vol. 1, No. 6). Namur: FUNDP. Namur center for complex systems.
Hubaux, Charles ; Libert, Anne-Sophie ; Carletti, Timoteo. / On the use of the MEGNO indicator with the global symplectic integrator. 6 ed. Namur : FUNDP. Namur center for complex systems, 2010. (naXys Technical Reports Series; 6).
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abstract = "To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced [Libert et al., 2010], based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In the present contribution, we show how to compute efficiently the MEGNO indicator jointly with the GSI. Moreover, we discuss the choice of symplectic integrator, in fact we point out that a particular attention has to be paid to the structure of the Hamiltonian system associated to the variational equations. The performances of our method is illustrated through the study of the Arnold diffusion problem.",
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Hubaux, C, Libert, A-S & Carletti, T 2010, On the use of the MEGNO indicator with the global symplectic integrator. naXys Technical Reports Series, no. 6, vol. 1, vol. 1, 6 edn, FUNDP. Namur center for complex systems, Namur.

On the use of the MEGNO indicator with the global symplectic integrator. / Hubaux, Charles; Libert, Anne-Sophie; Carletti, Timoteo.

6 ed. Namur : FUNDP. Namur center for complex systems, 2010. (naXys Technical Reports Series; Vol. 1, No. 6).

Research output: Book/Report/JournalOther report

TY - BOOK

T1 - On the use of the MEGNO indicator with the global symplectic integrator

AU - Hubaux, Charles

AU - Libert, Anne-Sophie

AU - Carletti, Timoteo

N1 - Publication code : FP SB092/2010/06 ; SB04977/2010/06

PY - 2010/11/29

Y1 - 2010/11/29

N2 - To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced [Libert et al., 2010], based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In the present contribution, we show how to compute efficiently the MEGNO indicator jointly with the GSI. Moreover, we discuss the choice of symplectic integrator, in fact we point out that a particular attention has to be paid to the structure of the Hamiltonian system associated to the variational equations. The performances of our method is illustrated through the study of the Arnold diffusion problem.

AB - To distinguish between regular and chaotic orbits in Hamiltonian systems, the Global Symplectic Integrator (GSI) has been introduced [Libert et al., 2010], based on the symplectic integration of both Hamiltonian equations of motion and variational equations. In the present contribution, we show how to compute efficiently the MEGNO indicator jointly with the GSI. Moreover, we discuss the choice of symplectic integrator, in fact we point out that a particular attention has to be paid to the structure of the Hamiltonian system associated to the variational equations. The performances of our method is illustrated through the study of the Arnold diffusion problem.

M3 - Other report

VL - 1

T3 - naXys Technical Reports Series

BT - On the use of the MEGNO indicator with the global symplectic integrator

PB - FUNDP. Namur center for complex systems

CY - Namur

ER -

Hubaux C, Libert A-S, Carletti T. On the use of the MEGNO indicator with the global symplectic integrator. 6 ed. Namur: FUNDP. Namur center for complex systems, 2010. (naXys Technical Reports Series; 6).