Wandering Flows on the Plane
Dynamical Systems
2025-04-18 v2 General Topology
Abstract
We study planar flows without non-wandering points and prove several properties of these flows in relation with their prolongational relation. The main results of this article are that a planar (regular) wandering flow has no generalized recurrence and has only two topological invariants: the space of its orbits and its prolongational relation (or, equivalently, its smallest stream). As a byproduct, our results show that, even in absence of any type of recurrence, the stream of a flow contains fundamental information on its behavior.
Keywords
Cite
@article{arxiv.2504.11751,
title = {Wandering Flows on the Plane},
author = {Joseph Auslander and Roberto De Leo},
journal= {arXiv preprint arXiv:2504.11751},
year = {2025}
}
Comments
32 pages, 6 figures