| Résume | Let f be a C^r Anosov diffeomorphism on T^2 and {f_1,...,f_k} be a family of C^r-random perturbations of f with r>2. We show that if the positive Lyapunov exponent of any stationary SRB measure of {f_1,...,f_k} is equal to the positive Lyapunov exponent of linearization A in GL(2,Z) of f, then the stable foliation of {f_1,...,f_k} are non-random and C^r-smooth. If we further assume the negative Lyapunov exponent of the stationary SRB measure also equals A, then there exists a smooth conjugacy h on T^2, such that h\circ f_i\circ h^{-1}=A+v_i for every i=1,...,k. The same result holds for random perturbations of generic hyperbolic automorphism A in GL(d,Z). This is a joint work with A. Brown. |
