High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913936461266944 |
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| author | Palmero, Matheus S. Graciano, Flavio H. Leonel, Edson D. de Oliveira, Juliano A. |
| author_facet | Palmero, Matheus S. Graciano, Flavio H. Leonel, Edson D. de Oliveira, Juliano A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well Palmero, Matheus S. Graciano, Flavio H. Leonel, Edson D. de Oliveira, Juliano A. Chaotic Dynamics 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. |
| title | High Energy States of Recurrent Chaotic Trajectories in Time-Dependent Potential Well |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.07801 |