The Teichmüller flow acts as a renormalization operator for interval exchange transformations. For this reason its properties give some insight about the dynamics of rational billiards. For example Lyapunov exponents of the Teichmüller flow are tightly related to equidistribution speed in rational billiards. Since the mid 90's M. Kontsevich and A. Zorich started computations of these exponents. After giving some motivating examples for the computation of these exponents and a brief overview of 30 years of intensive research (including works of A. Avila, A. Eskin, G. Forni, C. McMullen, M. Mirzakhani, W. Veech, A. Zorich, ...), I will show some details of the implementation of such computation in the package "surface_dynamics" inside SageMath.
Tue, 22/11/2016 - 14:00 to 15:00
Bet Belgia Library, Hebrew University of Jerusalem