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 dynamical systems  via a general piecewise spline maximum entropy method. We present a comparison of computations of Lyapunov exponents between a piecewise linear,  a piecewise quadratic and a piecewise cubic maximum entropy methods. In order to compute  Lyapunov exponents for deterministic maps,  we also compute density functions of their invariant measures via piecewise spline maximum entropy method.

Keywords

• Dynamical systems,General piecewise spline method,Invariant measure and invariant density,Lyapunov exponents,Maximum entropy optimization method

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