  It was proved by Brudno that entropy and Kolmogorov complexity for dynamical
systems are tightly related. We generalize his results to the case of arbitrary
computable amenable group actions. Namely, for an ergodic shift-action, the
asymptotic Kolmogorov complexity of a typical point is equal to the
Kolmogorov-Sinai entropy of the action. For topological shift actions, the
asymptotic Komogorov complexity of every point is bounded from above by the
topological entropy, and there is a point attaining this bound.
