The strong Palis conjecture for vector fields

Let $X$ be a vector field. A singular Axiom A vector field without cycle has only finitely many chain recurrent classes, each singular hyperbolic; a homoclinic tangency is a non-transversal intersection between the stable and unstable manifolds of a hyperbolic periodic orbit; and a heterodimensional cycle consists of two hyperbolic periodic orbits of different indices with the corresponding cyclic stable and unstable intersections. Strong Palis conjecture. Every vector field can be $C^r$ approximated by one of the following three kinds of vector fields: a vector field which is singular Axiom A without cycle, a vector field with a homoclinic tangency, or a vector field with a heterodimensional cycle. This is described as a continuation of Palis's conjectures for flows and is known in dimension three according to the source's attribution, while the general statement remains unresolved there.