A differentially algebraic replacement theorem, and analog computability

Authors:
Leonard Lipshitz and Lee A. Rubel

Journal:
Proc. Amer. Math. Soc. **99** (1987), 367-372

MSC:
Primary 12H05

Corrigendum:
Proc. Amer. Math. Soc. **104** (1988), 668.

MathSciNet review:
870803

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Abstract: A theorem is proved that enables one to replace a solution of a system of algebraic differential equations by analytic solutions nearby, such that each satisfies its own algebraic differential equation. As an application, we emend a proof of the Shannon-Pour-E1 thesis relating the outputs of analog computers to solutions of algebraic differential equations.

**[POE]**Marian Boykan Pour-el,*Abstract computability and its relation to the general purpose analog computer (some connections between logic, differential equations and analog computers)*, Trans. Amer. Math. Soc.**199**(1974), 1–28. MR**0347575**, 10.1090/S0002-9947-1974-0347575-8**[RUB]**Lee A. Rubel,*An elimination theorem for systems of algebraic differential equations*, Houston J. Math.**8**(1982), no. 2, 289–295. MR**674043****[SHA]**Claude E. Shannon,*Mathematical theory of the differential analyzer*, J. Math. Phys. Mass. Inst. Tech.**20**(1941), 337–354. MR**0006251**

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0870803-1

Article copyright:
© Copyright 1987
American Mathematical Society