Palis's conjecture on generic diffeomorphism dynamics

Let a diffeomorphism or non-singular line field be given, with genericity taken in the $C^1$ topology. Palis's conjecture. A $C^1$-generic diffeomorphism (or non-singular line field) either satisfies Axiom A, contains a robust heterodimensional cycle, or contains a robust homoclinic tangency. This conjecture revises Smale's dream by allowing robust non-hyperbolic phenomena; its general status is not specified in the source.