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The purpose of this article is to obtain dynamically coherence of partiallyhyperbolic diffeomorphisms in certain classes of Anosov diffeomorphisms onnilmanifolds, extending a result due to T. Fisher, R. Potrie and M. Sambarino[FPS] on the torus.

Dynamical coherence of partially hyperbolic diffeomorphisms on nilmanifolds isotopic to Anosov