Smale's generic Axiom A conjecture

Let $M$ be a compact manifold. A diffeomorphism of $M$ is Baire generic if it belongs to a countable intersection of open dense sets. Smale's conjecture. A Baire generic diffeomorphism of $M$ satisfies Axiom A. Smale's conjecture was intended to describe typical dynamical systems, but it was soon disproved by Smale and Smale–Abraham; Newhouse later exhibited open sets containing generic diffeomorphisms with infinitely many sinks.