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Recurrence-Based Characterization of Stickiness in Hamiltonian Systems

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Viana,  R. L.
External Organizations;

Souza,  L. C.
External Organizations;

Sales,  M. R.
External Organizations;

Mugnaine,  M.
External Organizations;

Szezech,  J. D.
External Organizations;

Caldas,  I. L.
External Organizations;

/persons/resource/Marwan

Marwan,  Norbert       
Potsdam Institute for Climate Impact Research;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Viana, R. L., Souza, L. C., Sales, M. R., Mugnaine, M., Szezech, J. D., Caldas, I. L., Marwan, N., Kurths, J. (2025): Recurrence-Based Characterization of Stickiness in Hamiltonian Systems. - In: Hirata, Y., Shiro, M., Fukino, M., Webber, C. L., Aihara, K., Marwan, N. (Eds.), - Recurrence Plots and Their Quantifications: Methodological Breakthroughs and Interdisciplinary Discoveries, (Springer Proceedings in Complexity), 10th International Symposium on Recurrence Plots (Tsukuba, Japan 2023), 95-108.
https://doi.org/10.1007/978-3-031-91062-3_6


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In quasi-integrable Hamiltonian systems, certain chaotic orbits become trapped around periodic islands for extended periods before escaping to the chaotic sea, a phenomenon known as stickiness. In fusion plasmas, the stickiness effect manifests in the prolonged trapping of magnetic field lines in a specific region for many toroidal turns, influencing plasma transport. We apply here a novel concept based on recurrence plots, revealing the existence of a hierarchical structure of islands around islands where chaotic orbits become trapped. This analysis is conducted for a Hamiltonian system describing the magnetic field lines in a Tokamak. Furthermore, utilizing this quantifier, we can distinguish between different levels of this structure and compute the cumulative distribution of trapping times.