96763 - Dynamical Systems

Learning outcomes

At the end of the course the student: - knows the fundamental aspects of the modern theory of dynamical systems (topological dynamics, ergodic theory, etc.) and can appreciate its motivations, both theoretical and applied; - is able to study certain elementary dynamical systems in depth; - is able to formulate dynamical problems in the appropriate mathematical terms.

Course contents

Tentative: Basic definitions and notions. Examples of dynamical systems and simple applications. Topological dynamics. Elements of measure theory. Ergodic theory. Entropy and Kolmogorov-Sinai entropy (rate). Basic concepts of hyperbolic dynamics and/or the method of the transfer operator for the statistical properties of dynamical systems and/or applications in mathematics and other sciences.

Readings/Bibliography

Notes taken in class are a necessary reference for this class. 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

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

More material will be posted here or on Virtuale as the course progresses.

Teaching methods

Classroom lectures.

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)

Teaching tools

Extra material (further readings, videos, etc.) might be suggested throughout the class and posted on Virtuale.

Office hours

See the website of Marco Lenci