  The article states that for every compact manifold M of dimension 4 or higher
there is an area U in a set of smooth diffeomorphisms over M such that every
map f from U has local maximal partially hyperbolic attractor and nonatomic
ergodic invariant measure on it where one of Lyapunov exponents vanish. The
result is first proved for skew products over horseshoe and then transferred
onto smooth diffeomorphisms.
