Analysis of round off errors with reversibility test as a dynamical indicator
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analysed suggests t...
| Autores principales: | , , |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2012
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/129367 |
| Aporte de: |
| id |
I19-R120-10915-129367 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Astronomía Física Discrete time dynamical systems Reversibility error Standard map LCE SALI GALI MEGNO mLCE |
| spellingShingle |
Astronomía Física Discrete time dynamical systems Reversibility error Standard map LCE SALI GALI MEGNO mLCE Faranda, Davide Mestre, Martín Federico Turchetti, Giorgio Analysis of round off errors with reversibility test as a dynamical indicator |
| topic_facet |
Astronomía Física Discrete time dynamical systems Reversibility error Standard map LCE SALI GALI MEGNO mLCE |
| description |
We compare the divergence of orbits and the reversibility error for discrete time dynamical systems. These two quantities are used to explore the behavior of the global error induced by round off in the computation of orbits. The similarity of results found for any system we have analysed suggests the use of the reversibility error, whose computation is straightforward since it does not require the knowledge of the exact orbit, as a dynamical indicator. The statistics of fluctuations induced by round off for an ensemble of initial conditions has been compared with the results obtained in the case of random perturbations. Significant differences are observed in the case of regular orbits due to the correlations of round off error, whereas the results obtained for the chaotic case are nearly the same. Both the reversibility error and the orbit divergence computed for the same number of iterations on the whole phase space provide an insight on the local dynamical properties with a detail comparable with other dynamical indicators based on variational methods such as the finite time maximum Lyapunov characteristic exponent, the mean exponential growth factor of nearby orbits and the smaller alignment index. For 2D symplectic maps the differentiation between regular and chaotic regions is well full-filled. For 4D symplectic maps the structure of the resonance web as well as the nearby weakly chaotic regions are accurately described. |
| format |
Articulo Preprint |
| author |
Faranda, Davide Mestre, Martín Federico Turchetti, Giorgio |
| author_facet |
Faranda, Davide Mestre, Martín Federico Turchetti, Giorgio |
| author_sort |
Faranda, Davide |
| title |
Analysis of round off errors with reversibility test as a dynamical indicator |
| title_short |
Analysis of round off errors with reversibility test as a dynamical indicator |
| title_full |
Analysis of round off errors with reversibility test as a dynamical indicator |
| title_fullStr |
Analysis of round off errors with reversibility test as a dynamical indicator |
| title_full_unstemmed |
Analysis of round off errors with reversibility test as a dynamical indicator |
| title_sort |
analysis of round off errors with reversibility test as a dynamical indicator |
| publishDate |
2012 |
| url |
http://sedici.unlp.edu.ar/handle/10915/129367 |
| work_keys_str_mv |
AT farandadavide analysisofroundofferrorswithreversibilitytestasadynamicalindicator AT mestremartinfederico analysisofroundofferrorswithreversibilitytestasadynamicalindicator AT turchettigiorgio analysisofroundofferrorswithreversibilitytestasadynamicalindicator |
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Repositorios |
| _version_ |
1764820452420616192 |