  We consider a certain two-parameter family of automorphisms of the affine
plane over a complete, locally compact non-Archimedean field. Each of these
automorphisms admits a chaotic attractor on which it is topologically conjugate
to a full two-sided shift map, and the attractor supports a unit Borel measure
which describes the distribution of the forward orbit of Haar-almost all points
in the basin of attraction. We also compute the Hausdorff dimension of the
attractor, which is non-integral.
