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Regular and Chaotic Dynamics

, Volume 24, Issue 1, pp 61–79 | Cite as

Vortex Pairs on the Triaxial Ellipsoid: Axis Equilibria Stability

  • Jair KoillerEmail author
  • César Castilho
  • Adriano Regis Rodrigues
Article
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Abstract

We consider a pair of opposite vortices moving on the surface of the triaxial ellipsoid E(a, b, c): x2/a+ y2/b+ z2/c = 1, a < b < c. The equations of motion are transported to S2 ×S2 via a conformal map that combines confocal quadric coordinates for the ellipsoid and sphero-conical coordinates in the sphere. The antipodal pairs form an invariant submanifold for the dynamics. We characterize the linear stability of the equilibrium pairs at the three axis endpoints.

Keywords

point vortices Riemann surfaces 

MSC2010 numbers:

76B99 34C28 37D99 
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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • Jair Koiller
    • 1
    Email author
  • César Castilho
    • 2
  • Adriano Regis Rodrigues
    • 3
  1. 1.Departamento de MatemáticaUniversidade Federal de Juiz de ForaJuiz de ForaBrazil
  2. 2.Departamento de MatemáticaUniversidade Federal de PernambucoRecifeBrazil
  3. 3.Universidade Federal Rural de PernambucoRecifeBrazil

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