Shearless bifurcations for two isochronous resonant perturbations
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909291772903424 |
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| author | Leal, Bruno B. Lazarotto, Matheus J. Mugnaine, Michele de Almeida, Alfredo M. Ozorio Viana, Ricardo L. Caldas, Iberê L. |
| author_facet | Leal, Bruno B. Lazarotto, Matheus J. Mugnaine, Michele de Almeida, Alfredo M. Ozorio Viana, Ricardo L. Caldas, Iberê L. |
| contents | In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of these secondary shearless curves is a standard process that may appear as control parameters are varied in situations where there is resonant mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic systems for the standard map, the Ullmann map, and for the Walker-Ford Hamiltonian flow. The onset of shearless curves is related to bifurcations of periodic points. Furthermore, depending on the bifurcation, these shearless curves can emerge alone or in pairs, and in some cases, deform into separatrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Shearless bifurcations for two isochronous resonant perturbations Leal, Bruno B. Lazarotto, Matheus J. Mugnaine, Michele de Almeida, Alfredo M. Ozorio Viana, Ricardo L. Caldas, Iberê L. Chaotic Dynamics In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of these secondary shearless curves is a standard process that may appear as control parameters are varied in situations where there is resonant mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic systems for the standard map, the Ullmann map, and for the Walker-Ford Hamiltonian flow. The onset of shearless curves is related to bifurcations of periodic points. Furthermore, depending on the bifurcation, these shearless curves can emerge alone or in pairs, and in some cases, deform into separatrices. |
| title | Shearless bifurcations for two isochronous resonant perturbations |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2408.10930 |