We show that any diffeomorphism of a compact manifold can be approximated by diffeomorphisms exhibiting a homoclinic tangency or by diffeomorphisms having a partial hyperbolic structure.
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Sylvain Crovisier, Martin Sambarino, Dawei Yang, Partial hyperbolicity and homoclinic tangencies. J. Eur. Math. Soc. 17 (2015), no. 1, pp. 1–49DOI 10.4171/JEMS/497