Recurrence time entropy and weak chaos in Hamiltonian flows
Abstract
Stickiness in mixed Hamiltonian systems causes chaotic trajectories to remain temporarily trapped near regular structures, making it difficult to distinguish regular, weakly chaotic, and strongly chaotic motion over finite times. We show that the recurrence time entropy (RTE), previously used in discrete maps, also characterizes weak chaos in Hamiltonian flows. In the Hénon-Heiles system, the RTE reproduces the structures identified by the largest Lyapunov exponent, taking intermediate values in the sticky layers, and yields a proportion of chaotic trajectories consistent with the smaller alignment index. The finite-time RTE identifies low-entropy episodes near regular islands, whose durations decay algebraically, whereas high-entropy episodes decay exponentially. The same characterization holds for a periodically driven system and for a Hamiltonian system with three degrees of freedom, whose section is four-dimensional. The RTE is thus an effective diagnostic of weak chaos and stickiness in Hamiltonian flows.
Versions
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BibTeX
@misc{sales2026recurrence,
title = {{Recurrence time entropy and weak chaos in Hamiltonian flows}},
author = {Matheus Rolim Sales and Leonardo Costa de Souza and Iberê Luiz Caldas and Edson Denis Leonel and José Danilo Szezech Jr},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.23501},
eprint = {2606.23501},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.23501},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Recurrence time entropy and weak chaos in Hamiltonian flows
AU - Matheus Rolim Sales
AU - Leonardo Costa de Souza
AU - Iberê Luiz Caldas
AU - Edson Denis Leonel
AU - José Danilo Szezech Jr
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2606.23501
UR - https://arxiv.org/abs/2606.23501
AB - Stickiness in mixed Hamiltonian systems causes chaotic trajectories to remain temporarily trapped near regular structures, making it difficult to distinguish regular, weakly chaotic, and strongly chaotic motion over finite times. We show that the recurrence time entropy (RTE), previously used in discrete maps, also characterizes weak chaos in Hamiltonian flows. In the Hénon-Heiles system, the RTE reproduces the structures identified by the largest Lyapunov exponent, taking intermediate values in the sticky layers, and yields a proportion of chaotic trajectories consistent with the smaller alignment index. The finite-time RTE identifies low-entropy episodes near regular islands, whose durations decay algebraically, whereas high-entropy episodes decay exponentially. The same characterization holds for a periodically driven system and for a Hamiltonian system with three degrees of freedom, whose section is four-dimensional. The RTE is thus an effective diagnostic of weak chaos and stickiness in Hamiltonian flows.
ER -