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We consider the adiabatic approximation as it is applied to a familiar class of infinite-dimensional equations. We show how this approximation may be directly invalidated by analyzing a statistical form of the eigenvalue equation before and after the adiabatic approximation is made. We introduce a statistical quantity which can be used to predict the existence of periodic windows in the chaotic regime

Stability Properties of Nonlinear Delay Systems and the Breakdown of the Adiabatic Approximation