  We show that the classical dynamics underlying the mean-field description of
homogeneous mixtures of spinor F=1 Bose-Einstein condensates in an external
magnetic field is integrable as a consequence of number conservation and axial
symmetry in spin space. The population dynamics depends only on the quadratic
term of the Zeeman energy and on the strength of the spin-dependent term of the
atom-atom interaction. We determine the equilibrium populations as function of
the ratio of these two quantities and the miscibility of the hyperfine
components in the ground state spinors are thoroughly discussed. Outside the
equilibrium, the populations are always a periodic function of time where the
periodic motion can be a libration or a rotation. Our studies also indicates
the absence of metastability.
