Lyapunov Exponents of One Dimensional Chaotic Dynamical Systems via a General Piecewise Spline Maximum Entropy Method

Abstract

In this paper, we study the computation of Lyapunov exponents for deterministic dynamicalsystems via a general piecewise spline maximum entropy method. We present a comparisonof computations of Lyapunov exponents between a piecewise linear, a piecewise quadraticand a piecewise cubic maximum entropy methods. In order to compute Lyapunov exponentsfor deterministic maps, we also compute density functions of their invariant measures viapiecewise spline maximum entropy method.