Lyapunov exponent for Lipschitz maps

It is well-known that the Lyapunov exponent plays a fundamental role in dynamical systems. In this note, we propose an alternative definition of Lyapunov exponent in terms of Lipschitz maps, which are not necessarily differentiable. We show that the results which are valid to standard discrete dynamical systems are also valid in this new context. Therefore, this novel approach expands the range of applications of the dynamical systems theory.