  The chaotic phenomenon of intermittency is modeled by a simple map of the
unit interval, the Farey map. The long term dynamical behaviour of a point
under iteration of the map is translated into a spin system via symbolic
dynamics. Methods from dynamical systems theory and statistical mechanics may
then be used to analyse the map, respectively the zeta function and the
transfer operator. Intermittency is seen to be problematic to analyze due to
the presence of an `indifferent fixed point'. Points under iteration of the map
move away from this point extremely slowly creating pathological convergence
times for calculations. This difficulty is removed by going to an appropriate
induced subsystem, which also leads to an induced zeta function and an induced
transfer operator. Results obtained there can be transferred back to the
original system. The main work is then divided into two sections. The first
demonstrates a connection between the induced versions of the zeta function and
the transfer operator providing useful results regarding the analyticity of the
zeta function. The second section contains a detailed analysis of the pressure
function for the induced system and hence the original by considering bounds on
the radius of convergence of the induced zeta function. In particular, the
asymptotic behaviour of the pressure function in the limit $\beta$, the inverse
of `temperature', tends to negative infinity is determined and the existence
and nature of a phase transition at $\beta=1$ is also discussed.
