Reconstructing the Jacobian from Data with Observational Noise

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Abstract
Methods for the determination of local dynamical linearization information from experimental time series data are subject to computational artifacts. We investigate the artifacts due to observational noise in the data, and give formulas for the expected values of the reconstructed Jacobian in some simple cases. The formulas we derive in the case of realistic noise amplitudes are quite different from those for the noiseless case. In turn, spurious Lyapunov exponents in the noisy case are correspondingly different from the noiseless case.

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