Impact Factor

César Castilho

Recife, PE, 50740-540 Brazil
Departamento de Matemática, Universidade Federal de Pernambuco


Koiller J., Castilho C., Rodrigues A. R.
Vortex Pairs on the Triaxial Ellipsoid: Axis Equilibria Stability
2019, vol. 24, no. 1, pp.  61-79
We consider a pair of opposite vortices moving on the surface of the triaxial ellipsoid $\mathbb{E}(a,b,c):$ $x^2/a+y^2/b+z^2/c=1, \, a < b < c$. The equations of motion are transported to $S^2 \times S^2$ 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
Citation: Koiller J., Castilho C., Rodrigues A. R.,  Vortex Pairs on the Triaxial Ellipsoid: Axis Equilibria Stability, Regular and Chaotic Dynamics, 2019, vol. 24, no. 1, pp. 61-79

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