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C8544 - DYNAMICAL SYSTEMS AND ERGODIC THEORY

Academic Year 2026/2027

                
                        Docente:
                        Marco Lenci
                    
                        Credits:
                        6
                    
                        SSD:
                        PHYS-06/A
                    
                        Language:
                        English
                    
                        Moduli:
                        
                            Marco Lenci
                            (Modulo 1)
                        
                            Marco Lenci
                            (Modulo 2)
                        
                        Teaching Mode:
                        
                                    In-person learning (entirely or partially) (Modulo 1); 
                                
                                    In-person learning (entirely or partially) (Modulo 2)
                                
                            Campus:
                            Bologna
                        
                            Corso:
                            Second cycle degree programme (LM) in
                            Physics (cod. 6695)

                                        Course Timetable
                                    
from Sep 16, 2026 to Dec 17, 2026

Learning outcomes

At the conclusion of the course, the student: - knows the fundamental principles of the mathematical theory of dynamical systems and the basic elements of the related ergodic theory; - appreciates the motivations and objectives underlying these theories, from both a theoretical and an applied viewpoint; - is capable of studying a number of elementary dynamical systems in detail; - is able to apply ideas and some techniques from the theory of dynamical systems to problems arising in other scientific disciplines.

Course contents

Very 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

To be modified and/or integrated:

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:

Storgatz, Nonlinear Dynamics and Chaos, CRC Press (3rd ed.)
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

Tentative:

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, software, etc.) will be suggested throughout the class and posted on Virtuale.

Office hours

See the website of Marco Lenci