Computation Of A Few Lyapunov Exponents For Continuous And Discrete Dynamical Systems

. In this paper, an error analysis of QR based methods for computing the first few Lyapunov exponents of continuous and discrete dynamical systems is given. Algorithmic developments are discussed. Implementation details, error estimators and testing are also given. 1. INTRODUCTION In this paper, we consider the computation of a few Lyapunov exponents for continuous and discrete finite dimensional dynamical systems. In [DRV2], we considered approximating all of the exponents of continuous dynamical systems, and gave error analysis and convergence results, as well as algorithmic details, for the class of QR based methods. Here we consider the case in which only the first few exponents are desired. As it turns out, the extension to this case is not automatic, and new theoretical and algorithmic aspects need to be addressed. We still focus on continuous and discrete QR methods, give convergence results, algorithmic details and testing. For continuous dynamical systems, a proper implement..