A new semi-analytic method confirms that leapfrogging four-vortex orbits lose stability at 1/alpha = phi^2, equivalently h_c = 1/8, via a rapidly converging Hill-determinant expansion.
Aref, Journal of Mathematical Physics 48, 065401 (2007), ISSN 0022-2488
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Stability of Leapfrogging Vortex Pairs: A Semi-analytic Approach
A new semi-analytic method confirms that leapfrogging four-vortex orbits lose stability at 1/alpha = phi^2, equivalently h_c = 1/8, via a rapidly converging Hill-determinant expansion.