Computation of Lyapunov Exponents for Dynamical System with Impact

International audienceConsider the dynamical system $\ddot u + 2\alpha \dot u + u = a\cos\omega t$ where the position $u$ is constrained to remain above an obstacle of height $u_\min$; when $u$ reaches the obstacle, its velocity is reversed and multiplied by a restitution coefficient $e \in [0, 1]$. For certain choices of parameters, the solutions are chaotic. We compute the Lyapunov exponents by three different methods, and we compare the results. The computation of these numbers is very sensitive to the method, and to the numerical parameters for a given method, even with a very accurate method