Morse Index and Stability of the Planar N-vortex Problem

@article{Hu2020MorseIA,
  title={Morse Index and Stability of the Planar N-vortex Problem},
  author={Xijun Hu and Alessandro Portaluri and Qin Xing},
  journal={Qualitative Theory of Dynamical Systems},
  year={2020}
}
This paper concerns the investigation of the stability properties of relative equilibria which are rigidly rotating vortex configurations sometimes called vortex crystals, in the N-vortex problem. Such a configurations can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hyper-surface in the phase space (topologically a pseudo-sphere whose coefficients are the circulation strengths of the vortices). Relative equilibria are generated by… 
2 Citations
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sind bisher Integrale der hydrodynamischen Gleichungen fast nur unter der Voraussetzung gesucht worden, dafs die rechtwinkligen Componenten der Geschwindigkeit jedes Wassertheilchens gleich gesetzt
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