On the error in approximating stability spectra for discrete dynamical systems

In this work, we develop a perturbation theory for the approximation of stability spectra (Lyapunov exponents and Sacker-Sell spectrum) for discrete time dynamical systems. The approach is based upon QR based methods that transform linear time varying discrete time systems to an upper triangular form that allows for extraction of the stability spectra. We focus on nonlinear planar maps and show how shadowing type error results can be combined with perturbation bounds for stability spectra. The utility of our results is illustrated with numerical experiments for the Hénon and standard maps.