A generic incompressible flow is topological mixing

Hyperbolicity in the volume-preserving scenario

“…We observe that the following version of Bonatti and Crovisier's result, Proposition 3.3, for incompressible flows can be found in [9]. Hence, together with the previous proposition, we obtain the following.…”

Generic Hamiltonian Dynamical Systems: An Overview

“…In the continuous-time case the first author proved in [7] the corresponding version for divergence-free flows, and recently Ferreira announced the following result. The main tool to conclude the proof of the previous result is the next theorem, a version for Hamiltonians of the connecting lemma for pseudo-orbits.…”

Helicity is the only invariant of incompressible flows whose derivative is continuous in the C 1 topology

“…By a result [7], the vector field B with i B µ = B can be C 1 -approximated by a sequence {B n } of topologically transitive divergence-free C 1 -vector fields on Q tangent to ∂Q. Since B is exact, it follows from the proof in [7] that B n can be chosen to be exact and having the same flux as B. Every such a 2-form B n can be ′′′ , i.e., it is equal to some constant h(c) depending only on c ∈ R (for some function h : R → R).…”

“…Polterovich and D. Peralta-Salas for their interest, useful discussions and indicating the papers [8] and [7].…”