  Analogues of the prime number theorem and Merten's theorem are well-known for
dynamical systems with hyperbolic behaviour. In this paper a 3-adic extension
of the circle doubling map is studied. The map has a 3-adic eigendirection in
which it behaves like an isometry, and the loss of hyperbolicity leads to
weaker asymptotic results on orbit counting than those obtained for hyperbolic
maps.
