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Lyapunov exponent spectrum

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In the region of state space near a strange attractor there must be a number of processes:  strong attraction to the attractor;  exponential divergence on the attractor (given by a Lyapunov exponent);  and the overall cycling around the attractor.

All these separate processes are quantified by the
spectrum of Lyapunov exponents---they refer to the dynamics of the chaos.