An Anosov diffeomorphism is topologically conjugate to an infranilmanifold automorphism if and only if it has polynomial Global Product Structure. 4297 License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 4298 ANDY HAMMERLINDL Theorem 1.3. For a (strongly) partially hyperbolic diffeomorphism on a 3-manifold M , the stable, center, and unstable foliations exist and are quasi-isometric if and only if M is finitely covered by the 3-torus. 2.

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... osov systems Definition. Consider a diffeomorphism f on a compact Riemannian manifold M with a • If E c is the zero bundle, then f is called Anosov. • If exactly one of E s and E u is the zero bundle, then f is called weakly partially hyperbolic. • If all three subbundles are non-zero, then f is called strongly partially hyperbolic.