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We consider simple Lyapunov-exponent-based conditions under which the response of a system to a chaotic drive is a smooth function of the drive state. We call this differentiable generalized synchronization (DGS). When DGS does not hold, we quantify the degree of nondifferentiability using the H\"older exponent. We also discuss the consequences of DGS and give an illustrative numerical example.
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Hunt et al. (1997) studied this question.
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