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Regular and Chaotic Dynamics

, Volume 23, Issue 5, pp 580–582 | Cite as

Relations Satisfied by Point Vortex Equilibria with Strength Ratio −2

  • Kevin A. O’Neil
Article
  • 15 Downloads

Abstract

Relations satisfied by the roots of the Loutsenko sequence of polynomials are derived. These roots are known to correspond to families of stationary and uniformly translating point vortices with two vortex strengths in ratio −2. The relations are analogous to those satisfied by the roots of the Adler–Moser polynomials, corresponding to equilibria with ratio −1. The proof uses an analysis of the differential equation that these polynomial pairs satisfy.

Keywords

point vortex polynomial equilibrium 

MSC2010 numbers

76B47 37F10 34M15 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe University of TulsaTulsaUSA

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