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Abstract: The binormal (or vortex filament) equation provides an approximation of the 3D incompressible Euler equation. We present a Hamiltonian framework for the binormal equation in higher-dimensions and its explicit solutions that collapse in finite time. By going to lower dimensions we observe a curious appearance of the golden ratio in the motion of point vortices in the half-plane. This is a joint work with C.Yang and H.Wang.
Alain Albouy,
Alain Chenciner,
Jacques Laskar