I'm attempting to characterize the chaotic nature of orbits for a dynamical system I'm studying. I've implemented some code which calculates the entire spectrum of Lyapunov exponents and works well for known systems like the Lorenz and Rossler systems. However, I'm not sure if it would apply for my dynamical system which has discontinuities in it. From my reading, it seems like Lyapunov exponents apply for smooth systems (from Oseledets theorem I believe). Do you know of any research or papers that describe if Lyapunov exponents can be used to characterize chaos for systems with discontinuities?
For some context, my system involves a free magnetic sphere making elastic collisions with a fixed sphere, and the discontinuities are from those collisions. I've used the code I've written to find Lyapunov exponents, but in looking at trajectories for stable states and unstable states (found from a previous research paper) the Lyapunov exponents seems to not describe the chaotic nature of those states very well.