Gevrey and analytic local models and normal forms for diffeomorphisms and vector fields

Abstract

The theme of this dissertation is situated in the study of dynamical systems. Dynamical systems are a very broad and general subject in mathematics and are used as a tool to solve problems in many sciences as physics, economics, biology, chemistry, . . . . In all these applications one is interested in the quantitative or qualitative behaviour of one or more variables that undergo a dynamical process. This process may be continuous or with discrete steps, and we focus in this dissertation on deterministic dynamical systems, i.e. the influence of noise and stochastic distortions is not considered. We will deal with two types of dynamical systems, vector fields and diffeomorphisms (on Cn).