34687 - Dynamical Systems and Applications

Learning outcomes

At the end of the course the student:
- knows some aspects and fundamental results of the modern theory of dynamical systems (such as topological dynamics, ergodic theory, entropy, etc.);
- is able to study in detail certain elementary dynamical systems;
- can use ideas and techniques from the theory of dynamical systems in certain applied fields (physics, biology, economics, medicine, linguistics, etc.).

Course contents

Basic definitions and notions. Examples od dynamical systems and simple applications. Topological dynamics. Elements of measure theory. Ergodic theory. Entropy and Kolmogorov-Sinai entropy (rate). Basic concepts od hyperbolic dynamics. Applications in mathematics and other sciences.

Readings/Bibliography

Notes taken in class are a necessary reference for this course. They will be complemented by some hand-outs and bibliographical references. The following are strongly recommended supporting textbooks:

• Walters, An introduction to ergodic theory, Springer, 1982
• Katok, Hasselblatt, A first course in dynamics, Cambridge U. Press, 2003

The notes by C. Ulcigrai, which can be found here, are also very useful. Other suggested textbooks are:

• Arnold, Avez, Ergodic Problems of Classical Mechanics, Addison-Wesley (Reprint ed. 1989)
• Katok, Hasselblatt, An introduction to the modern theory of dynamical systems, Revised ed., Cambridge U. Press, 1996

 

Teaching methods

Classroom lectures and recitations

Assessment methods

The exam consists of an oral examination and one of the following activities, chosen by the student:

• computer project, decided with the teacher (numerical computation, application, etc.)
• short seminar on a topic decided with the teacher (to be held in a different day than the oral exam)
• written exercise (on the same day as the exam)

 

Office hours

See the website of Marco Lenci