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arXiv · 2507.07801

High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well

Matheus S. Palmero·Flavio H. Graciano·Edson D. Leonel·Juliano A. de Oliveira
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Abstract

In this numerical study, recurrence quantification analysis of chaotic trajectories is explored to detect atypical dynamical behaviour in non-linear Hamiltonian systems. An ensemble of initial conditions is evolved up to a maximum iteration time, and the recurrence rate of each orbit is computed, allowing a subset of trajectories exhibiting significantly higher recurrences than the ensemble average to be identified. These special trajectories are determined through a suitable statistical distribution, within which peak detection reveals the respective initial condition that is evolved into a highly recurrent chaotic orbit, a phenomenon known as stickiness. By applying this methodology to a model of a classical particle in a time-dependent potential well, it is demonstrated that, for specific parameter values and initial conditions, such recurrent chaotic trajectories can give rise to transient high-energy states.

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Matheus S. Palmero, Flavio H. Graciano, Edson D. Leonel, Juliano A. de Oliveira. 2025-07-10. High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well. https://arxiv.org/abs/2507.07801

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