On 2-dimensional expanding attractors of A-flows

TL;DR

This paper constructs specific A-flows on closed manifolds of dimensions 3 and 4, demonstrating the existence of non-wandering sets composed of 2-dimensional expanding attractors, both orientable and non-orientable.

Contribution

It proves the existence of A-flows with prescribed 2-dimensional expanding attractors on closed manifolds of dimensions 3 and 4, including on the 3-sphere.

Findings

Existence of A-flows with 2D expanding attractors on 4-manifolds.

Existence of A-flows with non-orientable 2D attractors on 3-manifolds.

Construction of a nonsingular A-flow on the 3-sphere with an orientable 2D attractor.

Abstract

We prove that given any closed $n$-manifold $M^n$, $n\geq 4$, there is an A-flow $f^t$ on $M^n$ such that the non-wandering set $NW(f^t)$ consists of 2-dimensional expanding attractor (the both, orientable and non-orientable) and trivial basic sets. For 3-manifolds, we prove that given any closed 3-manifold $M^3$, there is an A-flow $f^t$ on $M^3$ such that the non-wandering set $NW(f^t)$ consists of a non-orientable 2-dimensional expanding attractor and trivial basic sets. Moreover, there is a nonsingular A-flow $f^t$ on a 3-sphere such that the non-wandering set $NW(f^t)$ consists of an orientable 2-dimensional expanding attractor and trivial basic sets (isolated periodic trajectories).