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

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.

Presented by W.A.Beyer

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© 1985 Springer-Verlag

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Beyer, W.A., Channell, P.J. (1985). A functional equation for the embedding of a homeomorphism of the interval into a flow. In: Liedl, R., Reich, L., Targonski, G. (eds) Iteration Theory and its Functional Equations. Lecture Notes in Mathematics, vol 1163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076412

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  • DOI: https://doi.org/10.1007/BFb0076412

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16067-0

  • Online ISBN: 978-3-540-39749-6

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