Wandering Flows on the Plane

2025/04/16 by Auslander, Joseph, De Leo, Roberto
#Dynamical Systems (math.DS) #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2504.11751

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.

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