Lyapunov Exponents without Rescaling and Reorthogonalization

Abstract

We present a new method for the computation of Lyapunov exponents utilizing representations of orthogonal matrices applied to decompositions of $M$ or $M\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{M}$ where $M$ is the tangent map. This method uses a minimal set of variables, does not require renormalization or reorthogonalization, can be used to efficiently compute partial Lyapunov spectra, and does not break down when the Lyapunov spectrum is degenerate.