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In this paper we will deal with Lipschitz continuous perturbations ofMorse-Smale semigroups with only equilibrium points as critical elements. Westudy the behavior of the structure of equilibrium points and their connectionswhen subjected to non-differentiable perturbations. To this end we define moregeneral notions of \emph{hyperbolicity} and \emph{transversality}, which do notrequire differentiability.

Lipschitz perturbations of Morse-Smale semigroups