Low-dimensional tori in Calogero-Moser-Sutherland systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911491145334784 |
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| author | Liashyk, Andrii Ma, Guorui Reshetikhin, Nicolai Sechin, Ivan |
| author_facet | Liashyk, Andrii Ma, Guorui Reshetikhin, Nicolai Sechin, Ivan |
| contents | The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata of dimensions $2s$, where $s = 0, 1, \ldots, n - 1$. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to $\mathbb{R}_{> 0}^s \times \mathbb{T}^s$. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low-dimensional tori in Calogero-Moser-Sutherland systems Liashyk, Andrii Ma, Guorui Reshetikhin, Nicolai Sechin, Ivan Exactly Solvable and Integrable Systems Mathematical Physics The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata of dimensions $2s$, where $s = 0, 1, \ldots, n - 1$. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to $\mathbb{R}_{> 0}^s \times \mathbb{T}^s$. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics. |
| title | Low-dimensional tori in Calogero-Moser-Sutherland systems |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics |
| url | https://arxiv.org/abs/2506.16610 |