Nonsingular structural stable chaotic 3-flows of attractor-repeller type
Abstract
We show that any orientable closed 3-manifold admits structurally stable non-singular flow whose non-wandering set consists of a 2-dimensional expanding attractor and finitely many repelling periodic trajectories. For , 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 , we show that there does not admit any structurally stable non-singular flow whose non-wandering set 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 ).
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}
}