On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909383878770688 |
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| author | Wei, Wenyin Knieps, Alexander Liang, Yunfeng |
| author_facet | Wei, Wenyin Knieps, Alexander Liang, Yunfeng |
| contents | Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of functional and functional derivative are borrowed from functional analysis to consider the whole system as an argument of the geometric representation of the periodic orbit or cycle. The shifts of an orbit/trajectory and periodic orbit/cycle are analyzed and concluded as formulae for maps/flows, respectively. The theory shall be beneficial for analyzing sensitivity to perturbations, and optimizing and controlling various systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits Wei, Wenyin Knieps, Alexander Liang, Yunfeng Dynamical Systems Functional Analysis Optimization and Control Chaotic Dynamics Plasma Physics Primary: 34D10 Secondary: 37D10, 37N05, 37N10, 37M21, 37J40, 37J46, 39A33, 39B52, 76W05, 78M30 Periodic orbits and cycles, respectively, play a significant role in discrete- and continuous-time dynamical systems (i.e. maps and flows). To succinctly describe their shifts when the system is applied perturbation, the notions of functional and functional derivative are borrowed from functional analysis to consider the whole system as an argument of the geometric representation of the periodic orbit or cycle. The shifts of an orbit/trajectory and periodic orbit/cycle are analyzed and concluded as formulae for maps/flows, respectively. The theory shall be beneficial for analyzing sensitivity to perturbations, and optimizing and controlling various systems. |
| title | On the shifts of orbits and periodic orbits under perturbation and the change of Poincaré map Jacobian of periodic orbits |
| topic | Dynamical Systems Functional Analysis Optimization and Control Chaotic Dynamics Plasma Physics Primary: 34D10 Secondary: 37D10, 37N05, 37N10, 37M21, 37J40, 37J46, 39A33, 39B52, 76W05, 78M30 |
| url | https://arxiv.org/abs/2407.08079 |