Local structural stability of actions of R-n on n-manifolds

Let M-m be a compact m-manifold and phi : R-n x M-m -> M-m a C-r, r >= 1, action with infinitesimal generators of class C-r. We introduce the concept of transversally hyperbolic singular orbit for an action phi and explore this concept in its relations to stability. Our main result says that if m = n and O-p is a compact singular orbit of phi that is transversally hyperbolic, then phi is C-1 locally structurally stable at O-p.