부산대학교 도서관

Consider the autonomous, first order difference equation [image omitted]  where the function f is analytic on its domain [image omitted] . Assume that this difference equation has at least one fixed point [image omitted] . A global first integral for this difference equation is an analytic function [image omitted] . If any of the fixed points are hyperbolic, then the only global first integral is the identically constant fuction. A global first integral exists if and only if the difference equation is invariant with respect to a one parameter Lie group of transformations. Existence of a nonconstant global first integral implies all the fixed points of the difference equation are nonhyperbolic.