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We present experimental results on the relaxation dynamics of vesicles subjected to a time-dependent elongation flow. We observed and characterized a new instability, which results in the formation of higher order modes of the vesicle shape (wrinkles), after a switch in the direction of the gradient of the velocity. This surprising generation of membrane wrinkles can be explained by the appearance of a negative surface tension during the vesicle deflation, due to compression in a sign-switching transient. Moreover, the formation of buds in the vesicle membrane has been observed in the vicinity of the dynamical transition point.

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