Differentiable conjugacies of Morse-Smale diffeomorphisms

We provide in this paper a complete set of invariants for differentiable conjugacies of Morse-Smale diffeomorphisms. In the setting of topological conjugacies, these diffeomorphisms play an important role similar to that of gradients whose singularities are non-degenerate and have their stable and unstable manifolds in general position: they exhibit a simple and yet stable dynamics, and they exist on every manifold PS]. Our main global invariant corresponds to a generalization of Mather's invariant for diffeomorphisms of the interval.