Stable and Unstable Manifolds

Abstract

In this chapter, we discuss the stable and unstable manifolds of an equilibrium point and of a fixed point. Stable and unstable manifolds are a useful tool for both the theorist and the simulator of nonlinear systems. As we shall see, under the proper conditions, the structure of the manifolds indicates the presence of Smale horseshoes which, in turn, implies sensitive dependence on initial conditions.