34687 - SISTEMI DINAMICI E APPLICAZIONI

Conoscenze e abilità da conseguire

Al termine del corso, lo studente: - conosce alcuni aspetti e risultati fondamentali della moderna teoria dei sistemi dinamici (quali possono essere la dinamica topologica, la teoria ergodica, l'entropia); - è in grado di studiare esaustivamente alcuni sistemi dinamici elementari; - è capace di usare idee e tecniche provenienti dalla teoria dei sistemi dinamici in certi ambiti applicativi (fisica, biologia, economia, medicina, linguistica, ecc.).

Contenuti

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.

Testi/Bibliografia

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.

Metodi didattici

Classroom lectures.

Modalità di verifica e valutazione dell'apprendimento

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)

Strumenti a supporto della didattica

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

Orario di ricevimento

Consulta il sito web di Marco Lenci