Reconstruction of dynamical and geometrical properties of chaotic attractors from threshold-crossing interspike intervals

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Abstract
We reconstruct the largest Lyapunov exponent and fractal dimension of a chaotic attractor using threshold-crossing interspike intervals alone. We show that in certain cases one may reconstruct from this data a set looking very similar to the initial attractor. We also give an explanation of this possibility based on the concept of instantaneous frequency.