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A functional equation for the embedding of a homeomorphism of the interval into a flow

  • W. A. Beyer
  • P. J. Channell
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1163)

Abstract

A functional equation φ(ω(x))=ω′(x)φ(x) for φ(x) is derived for the problem of finding φ so that for a given orientation-preserving everywhere-differentiable homeomorphism ω(x) of [0,1] with ω' ≠ 0, there exists a solution F(x,t) to Ft(x,t)=φ(F(x,t)) so that F(x,0)=x, F(x,1)=ω(x). A solution to the functional equation is given for the case where ω has a finite number of fixed points ai with ω'(ai) ≠ 1. The analogous equation in n-dimensional space is given.

Keywords

Functional Equation Analogous Equation Embedding Problem Iteration Theory Linear Functional Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • W. A. Beyer
    • 1
  • P. J. Channell
    • 1
  1. 1.Los Alamos National LaboratoryLos AlamosUSA

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