The weak Palis conjecture for vector fields

Let $X$ be a vector field, and let $C^r$ denote the differentiability topology. A horseshoe is the standard hyperbolic chaotic invariant set, and a Morse-Smale vector field has hyperbolic recurrent dynamics with transverse invariant-manifold intersections. Weak Palis conjecture. Every vector field can be $C^r$ approximated by a vector field with a horseshoe or by a Morse-Smale vector field. This is presented as a flow analogue of Palis's conjectures; the source later notes that the conjecture is proved for three-dimensional vector fields in the $C^1$ topology.