Codimension one generic homoclinic classes with interior
  We study generic diffeomorphisms with a homoclinc class with non empty interior and in particular those admitting a codimension one dominated splitting. We prove that if in the finest dominated splitting the extreme subbundles are one dimensional then the diffeomorphism is partially hyperbolic and from this we deduce that the diffeomorphism is transitive. 
Rafael Potrie, Martin Sambarino