Two Colored Diagrams for Central Configurations of the Planar Five-vortex Problem

TL;DR

This paper uses the singular sequence method to identify all two-colored diagrams that could indicate infinite stationary configurations in the planar five-vortex problem, advancing understanding of vortex configuration finiteness.

Contribution

The paper determines all two-colored diagrams relevant to the finiteness problem in the planar five-vortex problem using the singular sequence method.

Findings

Identified all two-colored diagrams for the five-vortex problem.

Provided a comprehensive set of potential scenarios for finiteness failure.

Enhanced understanding of stationary configuration finiteness in vortex dynamics.

Abstract

We apply the singular sequence method to investigate the finiteness problem for stationary configurations of the planar five-vortex problem. The initial step of the singular sequence method involves identifying all two-colored diagrams. These diagrams represent potential scenarios where finiteness may fail. We determined all such diagrams for the planar five-vortex problem.