A family of stable equilibria in bifurcation with spherical symmetry

SIAM J. Math. Anal. 23 (1992) 72-80

Ernest Barany and Ian Melbourne


It is shown that asymptotically stable branches of equilibria may generically bifurcate from a spherically symmetric solution that loses stability to spherical harmonics of order l for any odd l. The problem is reduced to one of evaluation of certain Clebsch-Gordan coefficients. The evaluation uses methods from the quantum mechanical theory of angular momentum.