Indicator Functions Detect Tangentially Transient Behaviour on Decaying Normally Hyperbolic Invariant Manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912304892739584 |
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| author | Montoya, Francisco Gonzalez Jung, Christof |
| author_facet | Montoya, Francisco Gonzalez Jung, Christof |
| contents | We study the decay scenario of a codimension-2 NHIM in a three degrees of freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincaré map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculated on a 2-dimensional plane in the phase space of the system. In addition, we observe the role of tangential transient effects on the decaying NHIM and their manifestation in the delay time indicator function. Thereby we obtain ideas on how the decay of NHIMs and the tangential transient effects are encoded in indicator functions. As an example of demonstration, we use the motion of an electron in a perturbed magnetic dipole field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02102 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Indicator Functions Detect Tangentially Transient Behaviour on Decaying Normally Hyperbolic Invariant Manifolds Montoya, Francisco Gonzalez Jung, Christof Chaotic Dynamics 37D10, 37D05, 37J20 We study the decay scenario of a codimension-2 NHIM in a three degrees of freedom Hamiltonian system under increasing perturbation when the NHIM loses its normal hyperbolicity. On one hand, we follow this decay in the Poincaré map for the internal dynamics of the NHIM. On the other hand, we also follow the decay in a time delay function calculated on a 2-dimensional plane in the phase space of the system. In addition, we observe the role of tangential transient effects on the decaying NHIM and their manifestation in the delay time indicator function. Thereby we obtain ideas on how the decay of NHIMs and the tangential transient effects are encoded in indicator functions. As an example of demonstration, we use the motion of an electron in a perturbed magnetic dipole field. |
| title | Indicator Functions Detect Tangentially Transient Behaviour on Decaying Normally Hyperbolic Invariant Manifolds |
| topic | Chaotic Dynamics 37D10, 37D05, 37J20 |
| url | https://arxiv.org/abs/2501.02102 |