DYNAMIC SYSTEMS

academic year 2025-2026

(MATHEMATICS)

Course begins September 30, 2025. Course ends December 19, 2025.

LECTURES (8 credits, 64 hours):
Tuesday 16-18, Room 1.
Thursday 16-18, Room 1.
Friday 16-18, Room 1.

OFFICE HOURS:
by appointment (just send me an e-mail).

ANNOUNCEMENTS:

The lecture of October 3, 2025 is cancelled

The lecture of October 24, 2025 is cancelled

The lecture of November 14, 2025 is cancelled

Syllabus
Prerequisites
Lecture Diary

Exams

Teaching Material

During the course I will post notes online covering the material taught in lectures. However, you are encouraged to also consult the books listed below.

The part on the qualitative study of Ordinary Differential Equations can be found in various books, for example, HIRSCH Morris W., SMALE Stephen, DIFFERENTIAL EQUATIONS, DYNAMICAL SYSTEMS, AND LINEAR ALGEBRA. This book also contains interesting exercises that would be very useful to do; the same applies to the exercises contained in the notes I will post during the course.
Many things, especially descriptive, can be found in the book "A First Course in Dynamics with a Panorama of Recent Developments" by Boris Hasselblatt and Anatole Katok, Cambridge University Press.
All of the material covered in the second part of the course (and much, much more) is available in Katok, Hasselblatt, INTRODUCTION TO MODERN DYNAMICAL SYSTEMS, Cambridge University Press.
A more compact version of part of the material covered can be found in the book Introduction to Dynamical Systems by Michael Brin and Garrett Stuck. (curiosity: Michael is the father of Sergey Brin, co-founder of Google).
For more on ergodic theory you can consult "Ergodic Theory with a View Towards Number Theory" by Manfred Einsiedler and Thomas Ward, or the classics "An Introduction to Ergodic Theory" by Peter Walters and/or "Ergodic Theory" by Karl E. Petersen.

COURSE NOTES (very preliminary and continually updated)
Provisional notes (read at your own risk)

Visualization of Dynamical Systems

To see the behavior of solutions of apparently simple Dynamical Systems, such as the standard map, you can use programs available online, for example one can be found by clicking here, another by clicking here, various mechanical systems can be found by clicking here. Others can be easily found using a search engine.
For a list of pages on dynamical systems, also containing visualization programs, you can click here.

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