A Structural Stability Theorem

Abstract

precise definition of structural stability given in ? 5 is somewhat stronger; it demands that the conjugacy 9q can be found within an arbitrary CO neighborhood of the identity when g is sufficiently close to f.) The idea of this definition is that qualitative properties of structurally stable diffeomorphisms are unchanged by small C' perturbations. The definition (or rather an analogous one for flows) was proposed by Andronov and Pontrjagin [2] in 1938. In this paper we prove that certain geometric conditions are sufficient for strutural stability. Our result is the following