Local Lyapunov Exponents and characteristics of fixed/periodic points embedded within a chaotic attractor

摘要

A chaotic dynamical system is characterized by a positive averaged exponential separation of two neighboring trajectories over a chaotic attractor. Knowledge of the Largest Lyapunov Exponent 1, of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (gamma_1>0) or not (gamma_1<0). We intended in this work to elaborate the connection between Local Lyapunov Exponents and the Largest Lyapunov Exponent where an alternative method to calculate A, has emerged. Finally, we investigated some characteristics of the fixed points and periodic orbits embedded within a chaotic attractor which led to the conclusion of the existence of chaotic attractors that may not embed in any fixed point or periodic orbit within it.