Markov partitions and homology for -solenoids

Given a relatively prime pair of integers, $n\geq m>1$ , there is associated a topological dynamical system which we refer to as an $n/m$ -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 $p$ -adic numbers. In the special case, $m=2,n=3$ and for $n>3m$ , 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 $n\geq m>1$ and relatively prime.