LYAPUNOV SPECTRA OF CORRELATED RANDOM MATRIX PRODUCTS

Abstract

We have numerically studied the Lyapunov spectra and the maximal Lyapunov exponent (MLE) in products of real symplectic correlated random matrices, each of which is produced by a modified Bernoulli map. As a statistical property, it has been well studied that the correlation function of the sequence of the map shows power-low decay. We can systematically investigate the influence of the correlation on the Lyapunov spectra and the fluctuation-strength dependence of the MLE. It is shown that the form of the scaled Lyapunov spectra does not change even if the correlation increases in the stationary region of the sequence, and in the nonstationary region, the form is quite different from the one in the stationary region. The power of the scaling law for the fluctuation-strength dependence of the MLE becomes small as the correlation increases, and a different scaling law can be observed in the strongly correlated nonstationary region as from the δ-correlated case.