  We present a numerical study of the magnetic field generated by an
axisymmetrically forced flow in a spherical domain. At small enough Reynolds
number, Re, the flow is axisymmetric and generates an equatorial dipole above a
critical magnetic Reynolds number Rmc . The magnetic field thus breaks
axisymmetry, in agreement with Cowling's theorem. This structure of the
magnetic field is however replaced by a dominant axial dipole when Re is larger
and allows non axisymmetric fluctuations in the flow. We show here that even in
the absence of such fluctuations, an axial dipole can also be generated, at low
Re, through a secondary bifurcation, when Rm is increased above the dynamo
threshold. The system therefore always find a way to bypass the constraint
imposed by Cowling's theorem. We understand the dynamical behaviors that result
from the interaction of equatorial and axial dipolar modes using simple model
equations for their amplitudes derived from symmetry arguments.
