Comparative study of variational chaos indicators and ODEs' numerical integrators

dc.creatorDarriba, Luciano Ariel
dc.creatorMaffione, Nicolás Pablo
dc.creatorCincotta, Pablo Miguel
dc.creatorGiordano, Claudia Marcela
dc.date2012-10
dc.date2020-04-16T14:25:31Z
dc.date.accessioned2023-07-14T19:20:05Z
dc.date.available2023-07-14T19:20:05Z
dc.identifierhttp://sedici.unlp.edu.ar/handle/10915/93530
dc.identifierhttp://www.worldscientific.com/doi/abs/10.1142/S0218127412300339
dc.identifierissn:0218-1274
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/7434899
dc.descriptionThe reader can find in the literature a lot of different techniques to study the dynamics of a given system and also, many suitable numerical integrators to compute them. Notwithstanding the recent work of Maffione et al. (2011a) for mappings, a detailed comparison among the widespread indicators of chaos in a general system is still lacking. Such a comparison could lead to select the most efficient algorithms given a certain dynamical problem. Furthermore, in order to choose the appropriate numerical integrators to compute them, more comparative studies among numerical integrators are also needed. This work deals with both problems. We first extend the work of Maffione et al. (2011) for mappings to the 2D H\'enon & Heiles (1964) potential, and compare several variational indicators of chaos: the Lyapunov Indicator (LI); the Mean Exponential Growth Factor of Nearby Orbits (MEGNO); the Smaller Alignment Index (SALI) and its generalized version, the Generalized Alignment Index (GALI); the Fast Lyapunov Indicator (FLI) and its variant, the Orthogonal Fast Lyapunov Indicator (OFLI); the Spectral Distance (D) and the Dynamical Spectras of Stretching Numbers (SSNs). We also include in the record the Relative Lyapunov Indicator (RLI), which is not a variational indicator as the others. Then, we test a numerical technique to integrate Ordinary Differential Equations (ODEs) based on the Taylor method implemented by Jorba & Zou (2005) (called taylor), and we compare its performance with other two well-known efficient integrators: the Prince & Dormand (1981) implementation of a Runge-Kutta of order 7-8 (DOPRI8) and a Bulirsch-St\"oer implementation. These tests are run under two very different systems from the complexity of their equations point of view: a triaxial galactic potential model and a perturbed 3D quartic oscillator.
dc.descriptionInstituto de Astrofísica de La Plata
dc.formatapplication/pdf
dc.format1-35
dc.languageen
dc.rightshttp://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rightsCreative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.subjectCiencias Astronómicas
dc.subjectChaos indicators
dc.subjectHamiltonian sytems
dc.subjectNumerical integrators
dc.subjectODES
dc.subjectVariational equations
dc.titleComparative study of variational chaos indicators and ODEs' numerical integrators
dc.typeArticulo
dc.typePreprint


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