The stability of the steady rotation of a system of three equidistant vortices outside a circle

A complete non-linear analysis of the stability of the steady rotation of three point vortices, placed in a plane at the vertices of a regular triangle outside a circular domain is carried out using the results of the Kolmogorov–Arnold–Moser theory. All the resonances of up to fourth order inclusive encountered here are listed and studied. The investigations of Havelock who solved this problem in a linear formulation are thereby completed.