On the error in computing Lyapunov exponents by QR Methods

We consider the error introduced using QR methods to approximate Lyapunov exponents. We give a backward error statement for linear non-autonomous systems, and further discuss nonlinear autonomous problems. In particular, for linear systems we show that one approximates a “nearby” discontinuous problem where how nearby is measured in terms of local errors and a measure of non-normality. For nonlinear problems we use a type of shadowing result.