Separatrix splitting through high-frequency non-smooth perturbations

Separatrices in integrable dynamical systems, if perturbed with analytic high frequency perturbations, split apart such that the splitting distance is exponentially small in the frequency parameter ω. This article utilizes a recent straightforward connection between the Melnikov function (which gives a measure of such a splitting) and a Fourier transform, to quantify such splitting under less smooth perturbations. If the perturbation is only piecewise C k spatially, the splitting distance goes as ω-k-1 for large ω. Copyright ©2007 Watam Press.Sanjeeva Balasuriyahttp://online.watsci.org/abstract_pdf/2007v14/v14n3a-pdf/3.pd