Smooth SVD on the Lorentz group with application to computation of Lyapunov exponents. (Q1426774)

The authors consider solutions of \(x'= A(t)x\), where \(A^+(t)D+ DA(t)= 0\), \(D= \left(\begin{smallmatrix} I_n & 0\\ 0 &-I_n\end{smallmatrix}\right)\) \(n\neq 0\neq n\), \(n\geq m\). They give an explicit constructive characterization of the singular value decomposition (SVD) of \(x\) using polar factorization. They consider a specific application in terms of approximating the Lyapunov exonents of \(x\) and give some numerical illustrations of their approach.