On the shifts of stable and unstable manifolds of a hyperbolic cycle under perturbation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913421862109184 |
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| author | Wei, Wenyin Hua, Jiankun Knieps, Alexander Liang, Yunfeng |
| author_facet | Wei, Wenyin Hua, Jiankun Knieps, Alexander Liang, Yunfeng |
| contents | Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control, are computable with minimal effort using functional derivatives by considering the entire system as an argument. The shifts of homoclinic and heteroclinic orbits, as the intersections of these manifolds, are readily calculated by analyzing the movements of the intersection points. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_06430 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the shifts of stable and unstable manifolds of a hyperbolic cycle under perturbation Wei, Wenyin Hua, Jiankun Knieps, Alexander Liang, Yunfeng Plasma Physics Dynamical Systems Functional Analysis Chaotic Dynamics Primary: 37D10, Secondary: 39A33, 39B52, 76W05, 78M30 Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control, are computable with minimal effort using functional derivatives by considering the entire system as an argument. The shifts of homoclinic and heteroclinic orbits, as the intersections of these manifolds, are readily calculated by analyzing the movements of the intersection points. |
| title | On the shifts of stable and unstable manifolds of a hyperbolic cycle under perturbation |
| topic | Plasma Physics Dynamical Systems Functional Analysis Chaotic Dynamics Primary: 37D10, Secondary: 39A33, 39B52, 76W05, 78M30 |
| url | https://arxiv.org/abs/2407.06430 |