Résume | Classical averaging theory for fast-slow systems allows to understand the behaviour of such a system for moderately long times. Yet, to understand the dynamics for longer times it is necessary to study the fluctuations around the average. This is a newer subject on which only partial results are known. I will illustrate in an example how a precise knowledge of the fluctuations allows to understand some of the statistical properties of the deterministic system by comparing it with a stochastic differential equation. |