In seminal papers Smale conjecture that most diffeomorphisms should have trivial centralizer. That is, maps commuting with the original dynamical systems are necessarily a power of it. Also, a similar conjecture about centralizers of smooth flows can be formulated. In this context, we present a result obtained with Paulo Varandas (UFBA) e Jorge Rocha (UP) about the existence of a open and dense subset of Komuro-expansive fields with singularities whose elements have quasi-trivial centralizer. We also introduce the concept of expansiveness to Rd-actions and describe the centralizer of this actions and present some examples and applications of our main results. |