First Integrals/Invariants & Symmetries for Autonomous Difference Equations (original) (raw)

This paper explores the existence and construction of first integrals/invariants for autonomous difference equations and their relationship to one-parameter Lie group symmetries. It presents a method to derive first integrals through the solution of a functional equation and demonstrates the connection with the symmetries of non-linear equations via illustrative examples. Future research directions include algorithm development for finding solutions to the functional equations using symbolic computation.