Transfer equivalence and reduction of nonlinear delta differential equations on homogeneous time scales

The problem of equivalence is considered for nonlinear single-input single-output systems defined on homogeneous time scales and described by n-th order input-output delta-differential equations. First the concepts of reduction and of irreducibility of an input/output equation are explained. Subsequently, based on these notions, a definition of equivalence is introduced, which generalizes the notion of transfer equivalence. A practical criterion for evaluating irreducibility is given in terms of subspaces of one-forms, classified according to their relative degrees.