Dynamics on Bi-Lagrangian Structures and Cherry maps
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915448720719872 |
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| author | Ndawa, Bertuel Tangue |
| author_facet | Ndawa, Bertuel Tangue |
| contents | We consider a bi-Lagrangian structure $(ω,\mathcal{F}_{1},\mathcal{F}_{2})$ on a manifold $M$, that is, $(M,ω,\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on $M$, and lift a dynamic on its tangent and cotangent bundles in different ways. In some cases, we show that the lifted structures are affine. In the case of the 2-dimensional torus, we find that an extension of the same dynamic on pairs of so-called Cherry vector fields induces a conjugation action on a subset of Cherry maps (circle maps with a flat). Additionally, we define the linear connections for certain Cherry maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics on Bi-Lagrangian Structures and Cherry maps Ndawa, Bertuel Tangue Dynamical Systems 53D05, 53D12 We consider a bi-Lagrangian structure $(ω,\mathcal{F}_{1},\mathcal{F}_{2})$ on a manifold $M$, that is, $(M,ω,\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on $M$, and lift a dynamic on its tangent and cotangent bundles in different ways. In some cases, we show that the lifted structures are affine. In the case of the 2-dimensional torus, we find that an extension of the same dynamic on pairs of so-called Cherry vector fields induces a conjugation action on a subset of Cherry maps (circle maps with a flat). Additionally, we define the linear connections for certain Cherry maps. |
| title | Dynamics on Bi-Lagrangian Structures and Cherry maps |
| topic | Dynamical Systems 53D05, 53D12 |
| url | https://arxiv.org/abs/2508.12350 |