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| The thermal convection of a pure fluid contained in a spherical shell rotating about a fixed axis is studied. The bifurcations from the conduction state give rise to azimuthal waves which have been computed by continuation methods, as steady solutions of a system for the waves, in the frame of reference of the spheres. Their stability has also been studied. We have found the coexistence of stable waves of different azimuthal wave number for the same value of the parameters of the problem due to the vicinity of a double-Hopf bfurcation. The eigenfunctions at the secondary bifurcation points reveal the nature of the modulation of the waves when they lose stability. If the waves are unstable, connecting orbits have been found by time integration, starting from the unstables states. |
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