A generic incompressible flow is topological mixing

Abstract

In this Note we prove that there exists a residual subset of the set of divergence-free vector fields defined on a compact, connected Riemannian manifold M, such that any vector field in this residual satisfies the following property: Given any two nonempty open subsets U and V of M, there exists τ ∈ R such that X t ( U ) ∩ V ≠ ∅ for any t ⩾ τ . To cite this article: M. Bessa, C. R. Acad. Sci. Paris, Ser. I 346 (2008).