Approximate controllability on the group of volume-preserving diffeomorphisms
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915750947586048 |
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| author | Agrachev, Andrei Kazandjian, Bettina |
| author_facet | Agrachev, Andrei Kazandjian, Bettina |
| contents | We study controlability issues for the group of volume-preserving diffeomorphisms of the torus $\mathbb T^d$ for system $\dot x=f(x)+u(t)$, where $f$ is a fixed divergence free vector field on $\mathbb T^d$ and $u(t)$ are constant vector fields which generate translations of the torus. Main results concern $d$ equals two or three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16939 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Approximate controllability on the group of volume-preserving diffeomorphisms Agrachev, Andrei Kazandjian, Bettina Optimization and Control Dynamical Systems We study controlability issues for the group of volume-preserving diffeomorphisms of the torus $\mathbb T^d$ for system $\dot x=f(x)+u(t)$, where $f$ is a fixed divergence free vector field on $\mathbb T^d$ and $u(t)$ are constant vector fields which generate translations of the torus. Main results concern $d$ equals two or three. |
| title | Approximate controllability on the group of volume-preserving diffeomorphisms |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2601.16939 |