A dichotomy for higher dimensional flows
  We analyze the dichotomy between {\em sectional-Axiom A flows} (c.f. \cite{memo}) and flows with points accumulated by periodic orbits of different indices. Indeed, this is proved for $C^1$ generic flows whose singularities accumulated by periodic orbits have codimension one. Our result improves \cite{mp1}. 
A. Arbieto, C. A. Morales
math.DS