Preprint A208/2003
Transitivity and homoclinic classes for singular hyperbolic systems

M. J. Pacifico | Morales, C. A.

**Keywords: **
transitivity | homoclinic classes

we study connected, singular hyperbolic, attractirng sets with dense closed orbits and only one singularity. These sets are shown to be transitive for most C^r flows. In general these sets are shown to be either transitive or the union of two homoclinic classes. In the later case we prove the existence of finitely many homoclinic classes.