Abstract:  AVERAGING PRINCIPLE

The averaging principle allows us to replace complicated equations by
simpler ones describing the same phenomenon.

The first lecture treats averaging for systems with random noise.
We describe the main results and provide several applications
including (some of) the following:

(1) If two companies sell an identical product could one of them
get a monopoly?

(2) How many people are likely to survive in a fight of equal
armies?

(3) If you got lost, is it better to wander randomly or to try
to remember the correct route?

The second lecture will discuss averaging for near integrable
Hamiltonian systems and the third one will review the general
theory of averaging in deterministic systems.