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On the perturbation of partially hyperbolic endomorphisms

Abstract We analyze when partially hyperbolic endomorphisms can be perturbed in order to be close to one with non-zero Lyapunov exponents and with an unique inverse measure. Problems of this nature were already boarded and solved in the setting of diffeomorphisms. The extension to non-invertible maps presents as one the main difficulties the fact of that multivaluated inverse iterations of the map make that the local unstable manifolds may intersect each other since they depend on the whole prehistory.