R6sum6. On 6tablit des majorations explicites de l'erreur de meilleure approximation polynomiale ainsi que des majorations explicites et nonexplicites de l'erreur d'interpolation de Lagrange, lorsque la fonction consid6r6e appartient /tun espace de Sobolev d'ordre non entier d6fini sur un ouvert born6 de ~".Les r6sultats obtenus g6ndralisent les r6sultats connus dans le cas des espaces de Sobolev d'ordre entier. Summary.Explicit bounds for the best polynomial approximation error, explicit and non-explicit bounds for the Lagrange interpolation error are derived for functions belonging to fractional order Sobolev spaces defined over a bounded open set in F,.".Thus the classical results of the integer order Sobolev spaces are extended.

We prove that the set of fiber-bunched SL(2, R)-valued Hölder cocycles with nonvanishing Lyapunov exponents over a volume preserving, accessible and center-bunched partially hyperbolic diffeomorphism is open. Moreover, we present an example showing that this is no longer true if we do not assume accessibility in the base dynamics.

In this work we address the problem of existence and uniqueness (finiteness) of ergodic equilibrium states for partially hyperbolic diffeomorphisms isotopic to Anosov on T 4 , with two-dimensional center foliation. To do so we propose to study the disintegration of measures along one-dimensional subfoliations of the center bundle. Moreover, we obtain a more general result characterizing the disintegration of ergodic measures in our context.