Families of Kuramoto models and bounded symmetric domains
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917510377373696 |
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| author | Olshanetsky, M. |
| author_facet | Olshanetsky, M. |
| contents | We define the families of Kuramoto models (KM) related to bounded symmetric domains. The families include the Lohe unitary model and the spherical models as special cases. Our approach is based on the construction proposed by Watanabe and Strogats WS. We replace the Poincare disc and its $S^1$ boundary in the WS construction on the bounded symmetric domains and on the its Bergman-Shilov (BS) boundaries. In Cartan classifications there are four classical domains of types I-IV. Here we consider the domains of types I,II and III. For a fixed domain there is a decreasing chain of the BS boundaries components. This leads to the KM families we described here. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06829 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Families of Kuramoto models and bounded symmetric domains Olshanetsky, M. Mathematical Physics Adaptation and Self-Organizing Systems We define the families of Kuramoto models (KM) related to bounded symmetric domains. The families include the Lohe unitary model and the spherical models as special cases. Our approach is based on the construction proposed by Watanabe and Strogats WS. We replace the Poincare disc and its $S^1$ boundary in the WS construction on the bounded symmetric domains and on the its Bergman-Shilov (BS) boundaries. In Cartan classifications there are four classical domains of types I-IV. Here we consider the domains of types I,II and III. For a fixed domain there is a decreasing chain of the BS boundaries components. This leads to the KM families we described here. |
| title | Families of Kuramoto models and bounded symmetric domains |
| topic | Mathematical Physics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2411.06829 |