Given a relatively prime pair of integers,
, there is associated a topological dynamical system which we refer to as an
-solenoid. It is also a Smale space, as defined by David Ruelle, meaning that it has local coordinates of contracting and expanding directions. In this case, these are locally products of the real and various
-adic numbers. In the special case,
, we construct Markov partitions for such systems. The second author has developed a homology theory for Smale spaces and we compute this in these examples, using the given Markov partitions, for all values of
and relatively prime.