Shearless barriers in the conservative Ikeda map
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912693812723712 |
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| author | Baroni, Rodrigo Simile de Carvalho, Ricardo Egydio Junior, José Danilo Szezech Caldas, Iberê Luiz |
| author_facet | Baroni, Rodrigo Simile de Carvalho, Ricardo Egydio Junior, José Danilo Szezech Caldas, Iberê Luiz |
| contents | We investigate the dynamics of the Ikeda map in the conservative limit, where it is represented as a two-dimensional area-preserving map governed by two control parameters, $θ$ and $ϕ$. We demonstrate that the map can be interpreted as a composition of a rotation and a translation of the state vector. In the integrable case ($ϕ= 0$), the map reduces to a uniform rotation by angle $θ$ about a fixed point, independent of initial conditions. For $ϕ\ne 0$, the system becomes nonintegrable, and the rotation angle acquires a coordinate dependence. The resulting rotation number profile exhibits extrema as a function of position, indicating the formation of shearless barriers. We analyze the emergence, persistence, and breakup of these barriers as the control parameters vary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_07322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shearless barriers in the conservative Ikeda map Baroni, Rodrigo Simile de Carvalho, Ricardo Egydio Junior, José Danilo Szezech Caldas, Iberê Luiz Chaotic Dynamics We investigate the dynamics of the Ikeda map in the conservative limit, where it is represented as a two-dimensional area-preserving map governed by two control parameters, $θ$ and $ϕ$. We demonstrate that the map can be interpreted as a composition of a rotation and a translation of the state vector. In the integrable case ($ϕ= 0$), the map reduces to a uniform rotation by angle $θ$ about a fixed point, independent of initial conditions. For $ϕ\ne 0$, the system becomes nonintegrable, and the rotation angle acquires a coordinate dependence. The resulting rotation number profile exhibits extrema as a function of position, indicating the formation of shearless barriers. We analyze the emergence, persistence, and breakup of these barriers as the control parameters vary. |
| title | Shearless barriers in the conservative Ikeda map |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2507.07322 |