ABSTRACT
This chapter introduces the definition of dynamical process, and the main ideas of the theory of dynamical systems and it investigates. It illustrates these ideas by examining some simple examples of dynamical processes generated by finite systems of ODEs and by iterated maps. The chapter proposes to give a first idea of the nature of the questions, related to the long time behavior of dynamical processes and it investigates. It presents two examples of continuous, finite dimensional dynamical systems, which admit an attractor for certain values of their parameters. The chapter describes values are found by numerical experiment; the existence of the attractor can be confirmed by the methods. However, the analytical complexity of these computations is such that it is far more effective to resort to numerical experimentation and geometric or topological arguments. Moreover, the uniformity of the rate of convergence of the orbits to the manifold makes these systems extremely stable under perturbations and numerical approximations.
