Corbes invariants en sistemes dinàmics forçats quasi-periòdicament

Abstract

[en] When studying a dynamic System, one of the best tools we have to describe its dynamics is the study of its fixed points. But when a system is disturbed in a quasi-periodic way, these points cease to exist, so the simplest elements we are left with to study are the invariant curves. The objective of this thesis is to discuss the existence of invariant curves in quasi-periodically forced dynamic systems, as well as providing an algorithm to compute them. If the system is reducible, we will study the dynamics of said curves. To reach this goal, we require an introduction to differential calculus in Banach spaces. We will address properties that are very similar to those already known in $\mathbb{R}$ or $\mathbb{C}$, in order to prove the Theorem of implicit function in Banach spaces.