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arXiv · 2506.16660

A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits

Javier Jiménez-López·Víctor J. García-Garrido
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Abstract

In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret, offering a direct and intuitive measure of dynamical behavior. We provide a heuristic argument linking its growth to the regularity or chaoticity due to the underlying initial condition, considering the arclength-based formulation of LDs. To evaluate its effectiveness, we benchmark it against more elaborate LD-based chaos indicators and the Smaller Aligment Index (SALI) using two prototypical systems: the H\'enon-Heiles system and the Chirikov Standard Map. Our results show that, despite its simplicity, the difference LD matches the accuracy of more sophisticated methods, making it a robust and accessible tool for chaos detection in dynamical systems.

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Javier Jiménez-López, Víctor J. García-Garrido. 2025-06-20. A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits. https://arxiv.org/abs/2506.16660

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