Dynamical Entropy for Z n -actions and Bogoliubov Automorphisms of the CAR-algebra

The notion of dynamical entropy for Z n -actions by automorphisms of C - algebras is studied. These results are applied to Bogoliubov actions of Z n on the CAR-algebra. It is shown that the dynamical entropy of Z n -Bogoliubov actions is computed by a formula analogous to that found by Stormer and Voiculescu in the case n = 1, and also it is proved that singular parts of these actions give zero contribution to the entropy. 1 Introduction The notion of entropy introduced by Kolmogorov [K] and Sinai [S] for transformations of a measure space is an important invariant in the ergodic theory. Connes, Narnhofer, Stormer and Thirring [CSt, C, CNT] defined and investigated the notion of dynamical entropy which is a natural generalization of Kolmogorov-Sinai entropy to automorphisms of operator algebras. In last years this entropy has been studied actively by many authors from different points of view (see the bibliography, for example, in [B, OP, St]). Some interesting applications o..