Comparative study of variational chaos indicators and ODEs' numerical integrators

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Fil: Darriba, Luciano A. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina

Detalles Bibliográficos
Autores principales: Darriba, Luciano A., Maffione, Nicolás Pablo, Cincotta, Pablo M., Giordano, Claudia M.
Lenguaje:Inglés
Publicado: 2012
Materias:
Astronomía
Chaos Indicators
Numerical Integrators
Variational Equations
ODEs
Hamil-tonian Systems
Acceso en línea:http://www.worldscientific.com/doi/abs/10.1142/S0218127412300339
http://hdl.handle.net/11336/42610
https://rid.unrn.edu.ar/jspui/handle/20.500.12049/2870
http://dx.doi.org/10.1142/S0218127412300339
Aporte de:
Repositorio Institucional Digital de la Universidad Nacional de Río Negro (UNRN) de Universidad Nacional de Río Negro
id I65-R171-20.500.12049-2870
record_format dspace
institution Universidad Nacional de Río Negro
institution_str I-65
repository_str R-171
collection Repositorio Institucional Digital de la Universidad Nacional de Río Negro (UNRN)
language Inglés
orig_language_str_mv eng
topic Astronomía
Chaos Indicators
Numerical Integrators
Variational Equations
ODEs
Hamil-tonian Systems
Astronomía
spellingShingle Astronomía
Chaos Indicators
Numerical Integrators
Variational Equations
ODEs
Hamil-tonian Systems
Astronomía
Darriba, Luciano A.
Maffione, Nicolás Pablo
Cincotta, Pablo M.
Giordano, Claudia M.
Comparative study of variational chaos indicators and ODEs' numerical integrators
topic_facet Astronomía
Chaos Indicators
Numerical Integrators
Variational Equations
ODEs
Hamil-tonian Systems
Astronomía
description Fil: Darriba, Luciano A. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina
author Darriba, Luciano A.
Maffione, Nicolás Pablo
Cincotta, Pablo M.
Giordano, Claudia M.
author_facet Darriba, Luciano A.
Maffione, Nicolás Pablo
Cincotta, Pablo M.
Giordano, Claudia M.
author_sort Darriba, Luciano A.
title Comparative study of variational chaos indicators and ODEs' numerical integrators
title_short Comparative study of variational chaos indicators and ODEs' numerical integrators
title_full Comparative study of variational chaos indicators and ODEs' numerical integrators
title_fullStr Comparative study of variational chaos indicators and ODEs' numerical integrators
title_full_unstemmed Comparative study of variational chaos indicators and ODEs' numerical integrators
title_sort comparative study of variational chaos indicators and odes' numerical integrators
publishDate 2012
url http://www.worldscientific.com/doi/abs/10.1142/S0218127412300339
http://hdl.handle.net/11336/42610
https://rid.unrn.edu.ar/jspui/handle/20.500.12049/2870
http://dx.doi.org/10.1142/S0218127412300339
work_keys_str_mv AT darribalucianoa comparativestudyofvariationalchaosindicatorsandodesnumericalintegrators
AT maffionenicolaspablo comparativestudyofvariationalchaosindicatorsandodesnumericalintegrators
AT cincottapablom comparativestudyofvariationalchaosindicatorsandodesnumericalintegrators
AT giordanoclaudiam comparativestudyofvariationalchaosindicatorsandodesnumericalintegrators
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spelling I65-R171-20.500.12049-28702023-05-18T17:10:21Z application/pdf info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/4.0/ 2012-05-08 Fil: Darriba, Luciano A. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina Fil: Darriba, Luciano A. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina Fil: Darriba, Luciano A. Instituto de Astrofísica La Plata; Argentina Fil: Maffione, Nicolas P. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina Fil: Maffione, Nicolas P. Instituto de Astrofísica La Plata; Argentina Fil: Maffione, Nicolas P. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina Fil: Cincotta, Pablo M. Instituto de Astrofísica La Plata; Argentina Fil: Cincotta, Pablo M. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata; Argentina Fil: Cincotta, Pablo M. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina Fil: Giordano, Claudia M. Instituto de Astrofísica de La Plata; Argentina. Fil: Giordano, Claudia M. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina Fil: Giordano, Claudia M. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina Comparative study of variational chaos indicators and ODEs' numerical integrators Darriba, Luciano A. Maffione, Nicolás Pablo Cincotta, Pablo M. Giordano, Claudia M. Astronomía Chaos Indicators Numerical Integrators Variational Equations ODEs Hamil-tonian Systems Astronomía true The 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. Darriba, Luciano A., Maffione, Nicolas P., Cincotta, Pablo M. & Giordano, Claudia M. (2012). Comparative study of variational chaos indicators and ODEs' numerical integrators (review). World Scientific; International Journal Of Bifurcation And Chaos; 22; 1-35 0218-1274 http://www.worldscientific.com/doi/abs/10.1142/S0218127412300339 http://hdl.handle.net/11336/42610 https://rid.unrn.edu.ar/jspui/handle/20.500.12049/2870 http://dx.doi.org/10.1142/S0218127412300339 eng 22 International Journal Of Bifurcation And Chaos

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