Estabilidade estrututal dos difeomorfismos de Anosov

Abstract

The present work represents my Master thesis in Pure Mathematics, next to the Federal University of Ceará. It is a structural stability of Anosov diffeomorphisms. The proof presented here is essentially contained in the work of K. W. Robbin in which the structural stability of the C2 diffeomorphisms satisfying the A-axiom and the condition of the strong transversality, defined on compact varieties, C-infinite, without edge, is demonstrated. We clarify that the structural stability of the Anosov diffeomorphisms is already a proven fact, what we do here is only to present a different proof, assuming that diffeomorphism is class C2, and using the demonstration of J. W. Robbin. In Chapter 1, we make a brief approach on the study of varieties, informing about the main things that will be used in our work. In Chapter 2, we introduced the Anosov diffeomorphisms, an example of such diffeomorphisms, and we also give the definition of structural stability. We conclude chapter 2 giving the ideas of the proof that will be developed in chapter 3. In Chapter 1, when we speak of varieties, we forget the mathematical rigor in the definitions a little, and in a less rigorous way, we only present the objects on which we work. I believe that this is a very reasonable attitude, since a detailed study of varieties would run away from the objectives of our work.