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A counterexample to elimination in systems of algebraic differential equations

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  26 February 2010

Lee A. Rubel
Lee A. Rubel
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 273, Altgeld Hall, 1409, West Green St., Urbana, Illinois, 60801, U.S.A.
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Extract

In line with the Ritt–Seidenberg elimination theorem in differential algebra [RIT], [SEI], and with an “approximation theorem” by Denef and Lipshitz [DEL] for formal power series, and with an elimination theorem by the author [RUB1] for C∞ solutions of systems of algebraic differential equations (ADE's), one is led to consider the corresponding elimination question for Cn solutions. Somewhat in the spirit of [RUB2], though, we produce a negative result in this direction.

MSC classification

Secondary: 34A99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 30 , Issue 1 , June 1983 , pp. 74 - 76
Copyright
Copyright © University College London 1983

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References

DEL.Denef, J. and Lipshitz, L.. Power series solutions of algebraic differential equations. Preprint, 1982.Google Scholar
RIT.Ritt, J. F.. Differential Algebra, Amer. Math. Soc. Colloquium Publications, 33 (1950).CrossRefGoogle Scholar
RUB1.Rubel, L. A.. An elimination theorem for systems of algebraic differential equations. Houston J. Math., 8 (1982), 289–295.Google Scholar
RUB2.Rubel, L. A.. Solutions of algebraic differential equations. J. Differential Equations, to appear.Google Scholar
SEI.Seidenberg, A.. An elimination theory for differential algebra. California University Publications in Mathematics (New Series), 3 (1955–60).Google Scholar