Construction of approximate invariants for non-integrable Hamiltonian systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908869157978112 |
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| author | Li, Yongjun Xu, Derong Hao, Yue |
| author_facet | Li, Yongjun Xu, Derong Hao, Yue |
| contents | We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI's fluctuation is actually a measure of chaos. Through minimizing the fluctuations with control knobs in accelerators, the stable region of long-term motions could be enlarged. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_07568 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of approximate invariants for non-integrable Hamiltonian systems Li, Yongjun Xu, Derong Hao, Yue Chaotic Dynamics Accelerator Physics We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn transformation maps in the form of a square matrix, AIs can be constructed order-by-order iteratively. Evaluating AI with simulation data, we observe that AI's fluctuation is actually a measure of chaos. Through minimizing the fluctuations with control knobs in accelerators, the stable region of long-term motions could be enlarged. |
| title | Construction of approximate invariants for non-integrable Hamiltonian systems |
| topic | Chaotic Dynamics Accelerator Physics |
| url | https://arxiv.org/abs/2501.07568 |