Symmetries and first integrals for nonlinear discrete-time systems

Abstract

In this paper, the concepts of Lie symmetry and of first integral for discrete-time nonlinear systems are discussed. Some results that hold for continuous-time nonlinear systems are extended to discrete-time ones. First, the strong relation between symmetries and first integrals is explored. Then the two concepts are studied separately, illustrating some applications of Lie symmetries and giving a computational procedure for the computation of first integrals.