  Despite the prominent importance of the Lyapunov exponents for characterizing
chaos, it still remains a challenge to measure them for large experimental
systems, mainly because of the lack of recurrences in time series analysis.
Here we develop a method to overcome this difficulty, valid for highly
symmetric systems such as systems with global coupling for which the
dimensionality of recurrence analysis can be reduced drastically. We test our
method numerically with two globally coupled systems, namely, logistic maps and
limit-cycle oscillators with global coupling. The evaluated exponent values are
successfully compared with the true ones obtained by the standard numerical
method. We also describe a few techniques to improve the accuracy of the
proposed method.
