The complete system of global integral and differential invariants for equi-affine curves

For the equi-affine group (epsilon)(n) of transformations of R^n, definitions of an (epsilon)(n)-equivalence of curves and an equiaffine type of a curve are introduced. The (epsilon)(n)-equivalence of curves is reduced to the problem of the (epsilon)(n)-equivalence of paths. A generating system of the differential ring of (epsilon)(n)invariant differential polynomial functions of curves is described. Global conditions of the (epsilon)(n)-equivalence of curves are given in terms of the equi-affine type of a curve and the generating differential invariants. An independence of the generating differential invariants is proved.