Functional Equation for the Embedding of a Homeomorphism of the Interval into a Flow

摘要

A functional equation phi( omega (x)) = omega '(x) phi(x) for phi(x) is derived for the problem of finding phi so that for a given orientation-preserving everywhere-differentiable homeomorphism omega (x) of (0,1) with omega ' not equal to 0, there exists a solution F(x,t) to F/sub t/(x,t) = phi(F) so that F(x,0) = x, F(x,1) = omega (x). A solution to the functional equation is given for the case where omega has a finite number of fixed points a/sub i/ with omega '(a/sub i/) not equal to 1. The analogus equation in n-dimensional space is given. 10 references. (ERA citation 10:006012)