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In this m\'emoire we study quasiperiodic cocycles in semi-simple compact Liegroups. For the greatest part of our study, we will focus ourselves toone-frequency cocyles. We will prove that $C^{\infty}$ reducible cocycles aredense in the $C^{\infty}$ topology, for a full measure set of frequencies.Moreover, we will show that every cocycle (or an appropriate iterate of it, ifhomotopy appears as an obstruction) is almost torus-reducible (i.e. can beconjugated arbitrarily close to cocycles taking values in an abelian subgroupof G). In the course of the proof we will firstly define two invariants of thedynamics, which we will call energy and degree and which give a preliminarydistinction between (almost-)reducible and non-reducible cocycles. We will thentake up the proof of the density theorem. We will show that an algorithm ofrenormalization converges to perturbations of simple models, indexed by thedegree. Finally, we will analyze these perturbations using methods inspired byK.A.M. theory.

Global aspects of the reducibility of quasiperiodic cocycles in semisimple compact Lie groups