Controllability of families of measure preserving vector fields
The author considers a family \(\Sigma\) of vector fields on a differentiable manifold M endowed with a probability measure m. The vector fields are assumed to preserve the measure m. The author proves that if \(\Sigma\) is transitive (i.e., if each point of M is reachable from each other along onward or backward trajectories of \(\Sigma)\) then for every initial point in an open dense and connected subset of M, the closure of the reachable set is equal to M. The paper also contains some examples.
vector fields on a differentiable manifold
scientific article; zbMATH DE number 4017737