Syllabus 2016

• Lecture 1.
  I'll discuss some generalities about dynamical systems and try to argue, via an explicit example, that predictability and isolated systems might be an illusion. I will describe briefly the phenomenological introduction of noise.
• Lecture 2.
  I will introduce a simple class of systems that will be used during the lectures to illustrate the ideas that I am trying to investigate. I will then show how an effective system can arise due to a time scale separation (Averaging).
• Lecture 3.
  I will show that, if one assumes that the initial conditions of the system are random, in a proper technical sense, then a brownian motion can arise providing a stochastic correction to the averaging previously discussed.
• Lecture 4.
  I will investigate the issue of the initial conditions and try to argue that, in fact, there is no need for any probabilistic assumptions (as done in the previous lecture) provided one asks the ``right” questions.

Bassam Fayad (Institut de Mathématiques de Jussieu)

• Lecture notes