Db. Fairlie et An. Leznov, THE INTEGRABLE MAPPING AS THE DISCRETE GROUP OF INNER SYMMETRY OF INTEGRABLE SYSTEMS, Physics letters. A, 199(5-6), 1995, pp. 360-364
It is shown that each integrable mapping is connected with a hierarchi
cal completely integrable sytem of equations of evolution type which a
re invariant with respect to the transformation described by this mapp
ing.