Robust estimation of tangent maps and Liapunov spectra

In this paper we describe three algorithms for estimating the spectrum of Liapunov exponents, which we have found to be robust and reasonably accurate when used in practical circumstances. Attention is focussed on least squares and total least squares methods for estimating tangent maps from time series data. The properties of the algorithms are demonstrated by application to a range of data sets: we consider numerical and experimental data, and discuss the effect of additive noise and system noise on the proposed methods.