- Docente: Marco Lenci
- Crediti formativi: 6
- SSD: MAT/07
- Lingua di insegnamento: Italiano
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
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Corso:
Laurea Magistrale in
Matematica (cod. 5827)
Valido anche per Laurea Magistrale in Matematica (cod. 8208)
Conoscenze e abilità da conseguire
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.
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
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