Numerical calculation of the lyapunov exponent for the logistic MAP

Chaotic maps can be used to describe the behavior of dynamical systems and they are characterized by a parameter. The logistic map (LM) is a chaotic map very used in different areas. In the analysis of the dynamical system an important feature is the system stability, which can be determined using the Lyapunov Exponent (LE). In this paper two ways to compute numerically the LE for the LM are shown. In the first alternative, the Birkhoffpsilas Ergodic Theorem (BET) and the orbit produced by the LM are used. In the second alternative, the stationary distribution rho_est of the LM is estimated using the first derived of the logistic function and the central values of each interval in the partition used in the estimation.