  Starting with a combinatorial partition theorem for words over an infinite
alphabet dominated by a fixed sequence, established recently by the authors, we
prove recurrence results for topological dynamical systems indexed by such
words. In this way we extend the classical theory developed by Furstenberg and
Weiss of dynamical systems indexed by the natural numbers to systems indexed by
words. Moreover, applying this theory to topological systems indexed by
semigroups that can be represented as words we get analogous recurrence results
for such systems.
