  A first analytic assessment of the role of anisotropic corrections to the
isotropic anomalous scaling exponents is given for the $d$-dimensional
kinematic magneto-hydrodynamics problem in the presence of a mean magnetic
field. The velocity advecting the magnetic field changes very rapidly in time
and scales with a positive exponent $\xi$. Inertial-range anisotropic
contributions to the scaling exponents, $\zeta_j$, of second-order magnetic
correlations are associated to zero modes and have been calculated
non-perturbatively. For $d=3$, the limit $\xi\mapsto 0$ yields
$\protect{\zeta_j=j-2+ \xi (2j^3 +j^2 -5 j - 4)/[2(4 j^2 - 1)]} $ where $j$
($j\geq 2$) is the order in the Legendre polynomial decomposition applied to
correlation functions. Conjectures on the fact that anisotropic components
cannot change the isotropic threshold to the dynamo effect are also made.

Chaotic Dynamics;Chaotic Dynamics