Many dynamical systems behave similarly to a stochastic process; they are (very loosely) called "chaotic".
The course aims to illustrate several different techniques for studying and making precise such phenomena.
I particular, I will discuss the following properties:
Such concepts will be investigated by analyzing classes of systems of increasing complexity. More precisely:
I will try to provide some notes for the material that cannot be easily found in print. Some of the topics can be found in:
The first is partially a review, so some topics are not treated in full detail. The second is much more detailed, although it covers less material. The third is a bit dated and covers only one dimensional maps, but it contains some nice facts. For material on the family of are preserving intermitted maps and birth of elliptic islands see here and here.
Here are some notes (for the students eyes only) that I hope may help. In particular, the appendices contain all the functional
analysis needed to follow the course.
I will updated them continuously, without warning, so check for the current version.
They are most likely full of mistakes, so read at your own risk.
I will try to upload more as we prooceed (but do not keep your hopes too high).