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For any manifold of dimension at least three, we give a simple construction of a hyperbolic invariant set that exhibits C1-persistent homoclinic tangency. It provides an open subset of the space of C 1 -diffeomorphisms in which generic diffeomorphisms have arbitrary given growth of the number of attracting periodic orbits and admit no symbolic extensions.

Hyperbolic sets exhibiting $C^1$-persistent homoclinic tangency for higher dimensions