  We prove a conjecture of K. Schmidt in algebraic dynamical system theory on
the growth of the number of components of fixed point sets. We also generalize
a result of Silver and Williams on the growth of homology torsions of finite
abelian covering of link complements. In both cases, the growth is expressed by
the Mahler measure of the first non-zero Alexander polynomial of the
corresponding modules. We use the notion of pseudo-isomorphism, and also tools
from commutative algebra and algebraic geometry, to reduce the conjectures to
the case of torsion modules. We also describe concrete sequences which give the
expected values of the limits in both cases. For this part we utilize a result
of Bombieri and Zannier (conjectured before by A. Schinzel) and a result of
Lawton (conjectured before by D. Boyd).
