<b>Local structural stability of actions of R^n on n-manifolds</b> - doi: 10.5269/bspm.v24i1-2.7435

Abstract

Let M^m be a compact m-manifold and  \varphi: R^n × M^m \rightarrow M^m a C^r, r \geq 1, action with infinitesimal generators of class C^r . We introduce the concept of transversally hyperbolic singular orbit for an action \varphi 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 \varphi that is transversally hyperbolic, then \varphi is C^1 locally structurally stable at O_p.