Finiteness of stationary configurations of the four-vortex problem

Hampton, Marshall; Moeckel, Richard

doi:10.1090/S0002-9947-08-04685-0

Finiteness of stationary configurations of the four-vortex problem
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by Marshall Hampton and Richard Moeckel PDF

Trans. Amer. Math. Soc. 361 (2009), 1317-1332 Request permission

Abstract:

We show that the number of relative equilibria, equilibria, and rigidly translating configurations in the problem of four point vortices is finite. The proof is based on symbolic and exact integer computations which are carried out by computer. We also provide upper bounds for these classes of stationary configurations.

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