Here is the video:
Discover dynamical systems !
- CHAOS : a mathematical adventure (free access online)
A series of nine 13-minute mathematical movies made by Jos Leys, Étienne Ghys and Aurélien Alvarez, in order to discover chaos in dynamical systems (This one can even be watched when you are still at school !)
- Dynamics done with your bare hands — series of four lectures on different subjects of dynamics (undergraduate level).
- Sergey Tabachnikov’s book « Geometry and billiards ». A good place to start in order to discover how mathematicians play pool (undergraduate level and maybe at school if motivated).
- Vladimir Arnold « Mathematical Methods of Classical Mechanics ». This book connects mathematics and physics questions together. I am regularly coming back to it. It’s
maybe a rough start but it is too much of a classic for me not to recommend it to a motivated undergraduate student. (Undergraduate, graduate and professor level :))
PS. For those of you who read French, I can’t resist to recommend a web-site Mathématiques du ciel on connection of dynamical systems with celestial mechanics, on which I have worked several years ago with Marie Lhuissier and Valentin Seigneur.
These choices are personal and non-objective. Please, choose the books and videos you like from this list and any other list, since everybody likes to learn in their own way!