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Persistent massive attractors of smooth maps

Abstract For a smooth manifold of any dimension greater than one, we present an open set of smooth endomorphisms such that any of them has a transitive attractor with a non-empty interior. These maps are m-fold non-branched coverings, m≥3. The construction applies to any manifold of the form S1×M, where S1 is the standard circle and Mis an arbitrary manifold.