Classification of linear periodic difference equations under periodic or kinematic similarity

In this paper linear periodic systems of difference equations are classifie d with respect to periodic similarity and kinematic similarity. Complete se ts of invariants of periodic difference equations relative to such similari ty transformations are given, and corresponding canonical forms are describ ed. Also the irreducible periodic difference equations, i.e., those that ca nnot be reduced by such similarities to a nontrivial direct sum, are identi fied.