Abstract: 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 λ₁ of a dynamical system over a bounded attractor is necessary and sufficient for determining whether it is chaotic (λ₁>0) or not (λ₁≤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 λ₁ 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.

Key words: Chaotic attractor, Largest Lyapunov Exponent, Local Lyapunov Exponents

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