DYNAMICAL ENTROPY FOR BOGOLIUBOV ACTIONS OF FREE ABELIAN-GROUPS ON THE CAR-ALGEBRA

The notion of dynamical entropy for actions of a countable free abelia n group G by automorphisms of C-algebras is studied. These results ar e applied to Bogoliubov actions of G on the CAR-algebra. It is shown t hat the dynamical entropy of Bogoliubov actions is computed by a formu la analogous to that found by Stormer and Voiculescu in the case G = Z , and also it is proved that the part of the action corresponding to a singular spectrum gives zero contribution to the entropy. The case of an infinite number of generators has some essential differences and r equires new arguments.