  We consider a dynamical system in R driven by a vector field -U', where U is
a multi-well potential satisfying some regularity conditions. We perturb this
dynamical system by a Levy noise of small intensity and such that the heaviest
tail of its Levy measure is regularly varying. We show that the perturbed
dynamical system exhibits metastable behaviour i.e. on a proper time scale it
reminds of a Markov jump process taking values in the local minima of the
potential U. Due to the heavy-tail nature of the random perturbation, the
results differ strongly from the well studied purely Gaussian case.
