The singular Axiom A or robust-cycle approximation conjecture

Let $X$ be a vector field. A singular Axiom A vector field without cycle has finitely many chain recurrent classes, each singular hyperbolic; a robustly heterodimensional cycle is a heterodimensional cycle persisting under perturbation. Singular Axiom A or robust-cycle conjecture. Every vector field can be $C^1$ approximated by a vector field which is singular Axiom A without cycle, or by a vector field with a robustly heterodimensional cycle. This is proposed as a further conjectural alternative in the spirit of Bonatti's conjectures; no resolution is supplied in the source.