  We prove an entropy formula for certain expansive actions of a countable
discrete residually finite group $\Gamma $ by automorphisms of compact abelian
groups in terms of Fuglede-Kadison determinants. This extends an earlier result
proved by the first author under somewhat more restrictive conditions.
  The main tools for this generalization are a representation of the $\Gamma
$-action by means of a `fundamental homoclinic point', and the description of
entropy in terms of the renormalized logarithmic growth-rate of the set of
$\Gamma_n$-fixed points, where $(\Gamma_n, n\ge1)$ is a decreasing sequence of
finite index normal subgroups of $\Gamma $ with trivial intersection.
