- Docente: Marco Lenci
- Credits: 6
- SSD: MAT/07
- Language: Italian
- Moduli: Marco Lenci (Modulo 1) Luca Marchese (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
Learning outcomes
At the end of the course the student: has a solid knowledge of certain geometric and analytic aspects of the theory of smooth dynamical systems (for example hyperbolic dynamics, dynamics in homogeneous and Teichmüller spaces, etc.); is able to conduct in full autonomy further studies within the subject area; is able to apply the acquired knowledge to questions in related fields, both theoretical and applied.
Course contents
Tentative syllabus:
Marchese: Geometry of the upper-half plane and action of SL(2,R). Geodesic and horocyclic flows. Fuchsian groups and quotients. Invariant measures and ergodic theory. Elements of Ratner theory.
Lenci: Hyperbolic dynamics: Local theory. Stable and unstable manifolds. Ralation with ergodic porperties. Elements of dynamics of hyperbolic billiards.
Readings/Bibliography
Suggested textbooks (list might be augmented):
- Einsiedler, Ward, Ergodic Theory with a view towards number theory, Springer, 2011
- Katok, Hasselblatt, An introduction to the modern theory of dynamical systems, Revised ed., Cambridge U. Press, 1996
- Brin, Stuck, Introduction to dynamical systems, Cambridge U. Press, 2003
Teaching methods
Classroom lectures.
Assessment methods
Two independent oral exams for the two parts. The final grade will be the average of the two grades.
Office hours
See the website of Marco Lenci
See the website of Luca Marchese