Abstract
We suggest an algorithm for the estimation of the largest Lyapunov exponent for one-dimensional domains. We evaluate the largest Lyapunov exponent for one-dimensional domains, which present the surrogate long-range correlated stochastic time series with Hurst exponent H=0.1, H=0.9, H=0.5. It has been established that for an anticorrelated time series with the Hurst exponent H=0.1, the largest Lyapunov exponent is positive. For a correlated time series with Hurst exponent H=0.9, the largest Lyapunov exponent is negative. Also for a classical random walk with Hurst exponent H=0.5, the largest Lyapunov exponent is close to zero