MARCEL GUARDIA 

Universitat Polit`ecnica de Catalunya, Spain 

Abstract : 

The Restricted Three Body Problem is the simplest model in Celestial Mechanics: it models the motion of a body with negligible mass under the influence of two massive bodies which move on ellipses. Its dynamics is extremely rich and far from completely understood. 

In this course I will explain how to construct chaotic dynamics for this model in different settings. To this end, we will introduce the classical Invariant manifolds and Melnikovs Theories, and we will show how to construct a Smale horseshoe (symbolic dynamics). We will apply all these techniques to the Restricted Three Body Problem. If time permitted, we will discuss how to apply these techniques when the model possesses different time scales and one has to face exponentially small phenomena.