Every compact manifold carries a completely hyperbolic diffeomorphism

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Abstract

We show that a smooth compact Riemannian manifold of dimension greater than or equal to 2 admits a Bernoulli diffeomorphism with non-zero Lyapunov exponents.

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Dolgopyat, D., & Pesin, Y. (2002). Every compact manifold carries a completely hyperbolic diffeomorphism. Ergodic Theory and Dynamical Systems, 22(2), 409–435. https://doi.org/10.1017/S0143385702000202

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