  We consider minimal, aperiodic symbolic subshifts and show how to
characterize the combinatorial property of bounded powers by means of a metric
property. For this purpose we construct a family of graphs which all
approximate the subshift space, and define a metric on each graph which extends
to a metric on the subshift space. The characterization of bounded powers is
then given by the Lipschitz equivalence of a suitably defined infimum metric
with the corresponding supremum metric. We also introduce zeta-functions and
relate their abscissa of convergence to various exponents of complexity of the
subshift.
