Approximate controllability on the group of volume-preserving diffeomorphisms

Andrei Agrachev; Bettina Kazandjian

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arXiv · 2601.16939

Approximate controllability on the group of volume-preserving diffeomorphisms

Andrei Agrachev·Bettina Kazandjian

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Abstract

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.

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Andrei Agrachev, Bettina Kazandjian. 2026-01-23. Approximate controllability on the group of volume-preserving diffeomorphisms. https://arxiv.org/abs/2601.16939

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