ENTROPY FOR RANDOM GROUP-ACTIONS

We consider the entropy of systems of random transformations, where th e transformations are chosen from a set of generators of a Z(d) action . We show that the classical definition gives unsatisfactory entropy r esults in the higher-dimensional case, i.e. when d greater than or equ al to 2. We propose a definition of the entropy for random group actio ns which agrees with the classical definition in the one-dimensional c ase, and which gives satisfactory results in higher dimensions. This d efinition is based on the fibre entropy of a certain skew product. We identify the entropy by an explicit formula which makes it possible to compute the entropy in certain cases.