Frequency Extraction from Invariant Flows
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914209053278208 |
|---|---|
| author | Xu, Derong Li, Yongjun Hao, Yue Nagaitsev, Sergei |
| author_facet | Xu, Derong Li, Yongjun Hao, Yue Nagaitsev, Sergei |
| contents | In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of integrable Hamiltonian systems. By treating invariants as generators of commuting Hamiltonian flows, the frequencies are obtained from time-of-flight parameters along these flows, providing a direct alternative to action-angle constructions and spectral methods based on long time series. The approach yields an explicit numerical procedure that extends naturally to systems with multiple degrees of freedom. Its effectiveness is demonstrated using the McMillan map, where machine-precision accuracy is achieved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frequency Extraction from Invariant Flows Xu, Derong Li, Yongjun Hao, Yue Nagaitsev, Sergei Exactly Solvable and Integrable Systems Accelerator Physics In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of integrable Hamiltonian systems. By treating invariants as generators of commuting Hamiltonian flows, the frequencies are obtained from time-of-flight parameters along these flows, providing a direct alternative to action-angle constructions and spectral methods based on long time series. The approach yields an explicit numerical procedure that extends naturally to systems with multiple degrees of freedom. Its effectiveness is demonstrated using the McMillan map, where machine-precision accuracy is achieved. |
| title | Frequency Extraction from Invariant Flows |
| topic | Exactly Solvable and Integrable Systems Accelerator Physics |
| url | https://arxiv.org/abs/2512.16060 |