  This thesis attempts to contribute to the study of differentiable dynamics
both from a semi-local and global point of view. The center of study is
differentiable dynamics in manifolds of dimension 3 where we are interested in
the understanding of the existence and structure of attractors as well as
dynamical and topological implications of the existence of a global partially
hyperbolic splitting. The main contributions are new examples of dynamics
without attractors where we get a quite complete description of the dynamics
around some wild homoclinic classes and two results on dynamical coherence of
partially hyperbolic diffeomorphisms of $\TT^3$.
