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We consider, on a compact manifold, the group of diffeomorphisms that areisotopic to the identity. We show that every recurrent element is a distorsionelement. This generalizes Avila's theorem on circle diffeomorphisms. The methodalso provides a new proof of a result by Calegari and Freedman: on a sphere, inthe group of homeomorphisms that are isotopic to the identity, every element isdistorted.

\'el\'ements de distorsion du groupe des diff\'eomorphismes isotopes \`a l'identit\'e d'une vari\'et\'e compacte