https://doi.org/10.1140/epjs/s11734-026-02183-4
Regular Article
Leveraging temporal features of the divergence quantifier of recurrence plot to detect chaos in conservative systems
1
Université de Toulon, Aix Marseille Univ, CNRS, CPT, Toulon, France
2
Institute of Physics and Astronomy, Eötvös University, Budapest, Hungary
a
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b
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Received:
21
October
2025
Accepted:
28
January
2026
Published online:
14
February
2026
Abstract
The recurrence-based divergence quantifier (DIV), traditionally applied to dissipative systems, is shown here to be an effective finite-time chaos indicator for conservative dynamics. We benchmark its performances against the well-established fast Lyapunov indicator (FLI), focusing on the standard map, a canonical model of Hamiltonian chaos. Through extensive numerical simulations on moderately long orbits, we find strong agreement between DIV and FLI, supporting the reported correlation between the divergence of recurrences and positive Lyapunov exponents. Additionally, our study sheds more light into asymptotic time properties of DIV by revealing distinct power laws on regular and chaotic components, both in the original and reconstructed phase spaces. In particular, on a regular component, the space average of DIV decays with the time N as 1/N, mirroring the decay rate of the maximal Lyapunov exponent. On chaotic components, the space average of DIV decreases at a much slower rate, close to 
. This scaling insight opens new avenues for characterizing chaos from time series. Our numerical results thus demonstrate DIV to be a computationally viable and theoretically rich tool for chaos detection in conservative systems.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
Jérôme Daquin and Tamás Kovács contributed equally to this work.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
