Functional equation for the embedding of a homeomorphism of the interval into a flow
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.
- Research Organization:
- Los Alamos National Lab., NM (USA)
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6171498
- Report Number(s):
- LA-UR-84-3089; CONF-8409172-1; ON: DE85000655
- Country of Publication:
- United States
- Language:
- English
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