Persistent massive attractors of smooth maps

Denis Volk

Published 2011-08-26, updated 2012-12-18Version 5

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, $m \ge 3$. The construction applies to any manifold of the form $S^1 \times M$, where $S^1$ is the standard circle and $M$ is an arbitrary manifold.