Massive evaluation and analysis of Poincaré recurrences (2018)

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Data creators : Ivan Shevchenko [1], Guillaume Rollin [2] [3], Alexander Melnikov [4], José Lages [2] [3]
[1] : Russian Academy of Sciences
[2] : Institut UTINAM (UMR 6213) (Université de Franche-Comté)
[3] : Observatoire des Sciences de l'Univers - Terre, Homme, Environnement, Temps, Astronomie (UAR 3245) (Université de Franche-Comté)
[4] : Tomsk State University
Description :
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincaré recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincaré recurrence method (PRM) and the custom Lyapunov characteristic exponent (LCE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such
as LCE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.
Disciplines :
physics, mathematical (physics), astronomy & astrophysics (sciences of the universe)

General metadata

Data acquisition date : from 2018 ongoing
Data acquisition methods :
Language : English (eng)
Formats : application/pdf, image/png, text/plain
Audience : Research
Publications :
  • Massive evaluation and analysis of Poincaré recurrences on grids of initial data: A tool to map chaotic diffusion (doi:10.1016/j.cpc.2019.106868)
Project and funder :
Record created 11 Jan 2019 by José Lages.
Last modification : 5 Sep 2019.
Local identifier: FR-18008901306731-2019-01-11.

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Université de Bourgogne, Université de Franche-Comté, UTBM, AgroSup Dijon, ENSMM, BSB, Arts des Metiers