  Motivated by results of recent analytic studies, we present a numerical
investigation of the late-time dynamics of scalar test fields on Kerr
backgrounds. We pay particular attention to the issue of mixing of different
multipoles and their fall-off behavior at late times. Confining ourselves to
the special case of axisymmetric modes with equatorial symmetry, we show that,
in agreement with the results of previous work, the late-time behavior is
dominated by the lowest allowed l-multipole. However the numerical results
imply that, in general, the late-time fall-off of the dominating multipole is
different from that in the Schwarzschild case, and seems to be incompatible
with a result of a recently published analytic study.
