Constructions of b-semitoric systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918132202864640 |
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| author | Brugués, Joaquim Hohloch, Sonja Mir, Pau Miranda, Eva |
| author_facet | Brugués, Joaquim Hohloch, Sonja Mir, Pau Miranda, Eva |
| contents | In this article, we introduce $b$-semitoric systems as a generalization of semitoric systems, specifically tailored for $b$-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinctive characteristics of these systems. A $b$-semitoric system is a 4-dimensional $b$-integrable system that satisfies certain conditions: one of its momentum map components is proper and generates an effective global $S^1$-action, and all singular points are non-degenerate and devoid of hyperbolic components. To illustrate this concept, we provide five examples of $b$-semitoric systems by modifying the coupled spin oscillator and the coupled angular momenta, and we also classify their singular points. Additionally, we describe the dynamics of these systems through the image of their respective momentum maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00560 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constructions of b-semitoric systems Brugués, Joaquim Hohloch, Sonja Mir, Pau Miranda, Eva Symplectic Geometry Mathematical Physics Dynamical Systems In this article, we introduce $b$-semitoric systems as a generalization of semitoric systems, specifically tailored for $b$-symplectic manifolds. The objective of this article is to furnish a collection of examples and investigate the distinctive characteristics of these systems. A $b$-semitoric system is a 4-dimensional $b$-integrable system that satisfies certain conditions: one of its momentum map components is proper and generates an effective global $S^1$-action, and all singular points are non-degenerate and devoid of hyperbolic components. To illustrate this concept, we provide five examples of $b$-semitoric systems by modifying the coupled spin oscillator and the coupled angular momenta, and we also classify their singular points. Additionally, we describe the dynamics of these systems through the image of their respective momentum maps. |
| title | Constructions of b-semitoric systems |
| topic | Symplectic Geometry Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2304.00560 |