English

Nonsingular structural stable chaotic 3-flows of attractor-repeller type

Dynamical Systems 2025-10-06 v1

Abstract

We show that any orientable closed 3-manifold MM admits structurally stable non-singular flow ftf^t whose non-wandering set NW(ft)NW(f^t) consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For M=S3M=\mathbb{S}^3, we prove that the set of repelling periodic trajectories can be an arbitrary link provided that this link contains the figure eight knot. When a link consists of a unique repelling periodic trajectory (not necessarily a figure eight knot), we prove that this trajectory cannot be a torus knot. For any closed 3-manifold MM, we show that there does not admit any structurally stable non-singular flow ftf^t whose non-wandering set NW(ft)NW(f^t) consists of a 2-dimensional expanding attractor and a repelling periodic trajectory so that the repelling periodic trajectory is a trivial knot (i.e., it bounds a disk in MM).

Keywords

Cite

@article{arxiv.2510.02704,
  title  = {Nonsingular structural stable chaotic 3-flows of attractor-repeller type},
  author = {Zhentao Lai and V. Medvedev and Bin Yu and E. Zhuzhoma},
  journal= {arXiv preprint arXiv:2510.02704},
  year   = {2025}
}
R2 v1 2026-07-01T06:14:41.381Z