Dataset : Massive evaluation and analysis of Poincaré recurrences

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Ivan Shevchenko ; Guillaume Rollin ; Alexander Melnikov ; José Lages (2018): Massive evaluation and analysis of Poincaré recurrences. Institut UTINAM (UMR 6213). doi:10.25666/DATAOSU-2019-01-11

General metadata

Identifier : local : FR-18008901306731-2019-01-11 external : doi:10.25666/DATAOSU-2019-01-11
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)
Keywords :

Dates :
Data acquisition : from 2018 ongoing
Data provision : 1 Jan 2018
Metadata record :
Creation : 11 Jan 2019
Update : 5 Sep 2019

Language : English (eng)
Audience : Research

Administrative metadata

Data creatorsAffiliation
Ivan ShevchenkoRAS (RUS)
Guillaume RollinUTINAM (FRA)
Alexander MelnikovTSU (RUS)
José LagesUTINAM (FRA)
Publisher : Institut UTINAM (UMR 6213)
Science contact : José Lages website e-mail
Computing contact : José Lages website e-mail
Project and funder :
Access : available

Technical metadata

Formats : application/pdf, image/png, text/plain
Data acquisition methods :
Datatype : Dataset


  • 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)
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