An introduction to chaotic dynamics, with some applications

In this lectures we will present a brief introduction to chaotic dynamics, together with some applications, according to the following outline:

1) A brief historical introduction
2) Different concepts of chaos
3) A paradigmatic example: the "Bernoulli shift"
4) The Smale horseshoe
5) Topological horseshoes
6) Fixed points and periodic points for contractive/expansive maps
7) A topological method for seeking chaotic dynamics
8) "Linked Twist Maps"
9) Some applications, topological fluid mixing, fluid stirring