Mane genericity theorem for differentiable maps

Smale [16] posed the following question; is having an attracting periodic orbit a generic property for diffeomorphisms of two-sphere $S^2\ulcorner$(A generic property of $f \in Diff(M)$ is one that is true for a Baire set in Diff(M)). Mane[5] and Plykin[13] had an positive answer for Axiom A diffeomorphisms of $S^2$. To explain our theorem, we begin by briefly recalling stability conjecture posed by palis and smale.