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)


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.


Functional Equation Analogous Equation Embedding Problem Iteration Theory Linear Functional Equation 
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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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