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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Finiteness of stationary configurations of the four-vortex problem


Authors: Marshall Hampton and Richard Moeckel
Journal: Trans. Amer. Math. Soc. 361 (2009), 1317-1332
MSC (2000): Primary 70F10, 70F15, 37N05, 76Bxx
Published electronically: October 16, 2008
MathSciNet review: 2457400
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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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Additional Information

Marshall Hampton
Affiliation: School of Mathematics, University of Minnesota, Duluth, Minnesota 55812
Email: mhampton@d.umn.edu

Richard Moeckel
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: rick@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04685-0
PII: S 0002-9947(08)04685-0
Keywords: Relative equilibria, vortices
Received by editor(s): December 15, 2006
Published electronically: October 16, 2008
Additional Notes: The first author was partially supported by NSF grant DMS-0202268. The second author was partially supported by NSF grant DMS-0500443.
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.