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**Nonlinear stability analysis of a regular vortex pentagon outside a circle.**
*(English)*
Zbl 1252.76017

Summary: A nonlinear stability analysis of the stationary rotation of a system of five identical point vortices lying uniformly on a circle of radius \(R_0\) outside a circular domain of radius \(R\) is performed. The problem is reduced to the problem of stability of an equilibrium position of a Hamiltonian system with a cyclic variable. The stability of stationary motion is interpreted as Routh stability. Conditions for stability, formal stability and instability are obtained depending on the values of the parameter \(q = R^2/R^2_0\).

### MSC:

76B47 | Vortex flows for incompressible inviscid fluids |

34D20 | Stability of solutions to ordinary differential equations |

70K30 | Nonlinear resonances for nonlinear problems in mechanics |

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\textit{L. G. Kurakin} and \textit{I. V. Ostrovskaya}, Regul. Chaotic Dyn. 17, No. 5, 385--396 (2012; Zbl 1252.76017)

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### References:

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