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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References
Coddington, E.A., Levinson, N.: Theory of Ordinary Differential Equations, McGraw-Hill, 1955, p.10.
Coifman, R.R., Kuczma, M.: On Asymptotically Regular Solutions of a Linear Functional Equation, Aequationes Mathematicae 2, 332–336 (1969).
Kuczma, M.: Functional Equations in a Single Variable, Polska Akademia Nauk, Monografie Matematyczne (1968).
Kucma, M., Choczewski,and Ger, R.: Iterative Functional Equations, to be published by Cambridge University Press.
McKiernan, M.A.: On the Convergence of Series of Iterates, Publicationes Mathematicae Debrece, 10, 30–39 (1963).
Palis, J.: Vector fields generate few maps, Bull. Amer. Math. Soc., 80, 503–505 (1974).
Targonski, Gy.: Topics in Iteration Theory, Vandenhoeck and Ruprecht, Göttingen, Zürich, p.89 ff. (1981).
Targonski, Gy.: New Directions and Open Problems in Iteration Theory, Bericht Nr.229 (1984), Mathematisch-Statistische Sektion im Forschungszentrum Graz, Austria, 1984.
Utz, W.R.: The embedding of homoemorphisms in continuous flows, Topology Proceedings 6, 159–177 (1981).
Zdun, M.C.: Differentiable Fractional Iteration, Bull.Acad.Pol.Sci., sér.sci. math.astr.et phys., 25, 643–646 (1977).
Zdun, M.: Continuous and differentiable iteration semigroups, Prace Naukowe Uniwersitetu Śląskiego w Katowicach Nr.308 (1979).
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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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