Möbius Transformations: Properties and Applications

This lecture, given by the instructor Malo Jézéquel, covers Möbius transformations in the context of SL(2, R). The lecture explores the properties of hyperbolic elements, fixed points, and the ping-pong lemma. It delves into the concept of bounded distortion and its implications, showcasing the factorization of Möbius transformations. The lecture concludes with a discussion on the Patterson-Sullivan measure and its role in understanding d-regularity. Throughout the lecture, various exercises are presented and solved to illustrate the theoretical concepts discussed.