Denseness of morse-smale systems on surfaces

Abstract

Let M be a compact, connected 2-manifold without boundary. Morse-Smale fields are known to be dense in the space of all Cr vector elds on M when M is oriented or is one of RP2, Klein bottle or torus with a cross cap. In this work, we study the proofs of these facts. Furthermore, we exhibit a global picture of a Cr vector eld X on a compact, connected 2-manifold without boundary when all the singularities of X are hyperbolic.