Determination Lyapunov exponents in deterministic dynamical systems (Q1298203)

The goal of this paper is to estimate the Lyapunov exponent of the ergodic dynamical system determined by the equation \(x_t=\phi(x_{t-1})\) from observations \(x_1,\dots,x_n\). The authors propose two different estimates of the map \(\phi\) and its derivative based on the nearest neighbor method, prove the consistency of estimates and use them to construct the estimates of Lyapunov exponents. The proposed methodology is justified by simulations in two cases of the logistic function and \(p\)-adic map.