  The effect on dynamo action of an anisotropic electrical conductivity
conjugated to an anisotropic magnetic permeability is considered. Not only is
the dynamo fully axisymmetric, but it requires only a simple differential
rotation, which twice challenges the well-established dynamo theory. Stability
analysis is conducted entirely analytically, leading to an explicit expression
of the dynamo threshold. The results show a competition between the anisotropy
of electrical conductivity and that of magnetic permeability, the dynamo effect
becoming impossible if the two anisotropies are identical. For isotropic
electrical conductivity, Cowling's neutral point argument does imply the
absence of an azimuthal component of current density, but does not prevent the
dynamo effect as long as the magnetic permeability is anisotropic.
