Hyperbolic Fixed Points of Diffeomorphisms and Their Stable and Unstable Manifolds

Abstract

The most common kind of dynamical system is that coming from a differential equation since it is most commonly differential equations which are used to model physical processes. However, as we shall see later in this book, the study of the dynamical properties of a differential equation can often be reduced to the study of the properties of a diffeomorphism. Diffeomorphisms are also of interest in themselves since they can be used as discrete models of physical and biological processes. Also in some ways they are easier to study than differential equations. For these reasons, we begin this book with the study of diffeomorphisms.