Persistent massive attractors of smooth maps

TL;DR

This paper constructs an open set of smooth maps on manifolds of dimension greater than one that have transitive attractors with non-empty interior, revealing complex dynamical behaviors in high-dimensional smooth systems.

Contribution

It introduces a new class of smooth endomorphisms with persistent transitive attractors with interior, applicable to manifolds of the form S^1 x M, expanding understanding of attractor structures.

Findings

Existence of open sets of smooth maps with transitive attractors with interior.

Construction of such maps as m-fold non-branched coverings for m ≥ 3.

Applicability to manifolds of the form S^1 x M.

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, $m \ge 3$. 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.