Experimental Mathematics with Python: Calculating Lyapunov exponents of non-elastic billiard models
Authors: Alonso Espinosa & David P. Sanders* (presenter) Institution: Department of Physics, Faculty of Sciences, Universidad Nacional Autónoma de México (UNAM)
We discuss the calculation of quantities in a chaotic dynamical system which measure how chaotic the dynamics is, namely the Lyapunov exponents. This calculation is applied to a point bouncing inside an equilateral triangle (a billiard-type model), but with a non-elastic collision at the boundary. The mathematical understanding of this system, including a detailed description of the dynamics, came as a result of exploring the dynamics computationally. It exhibits strange attractors which undergo a series of qualitative changes as the non-elasticity parameter is varied.