Rational approximation to solutions of algebraic differential equations
نویسندگان
چکیده
منابع مشابه
Solutions of Algebraic Differential Equations
This paper may be considered as a mathematical essay on the question “What is a solution of an algebraic differential equation?” Many theorems in differential algebra are proved by differentiating an algebraic differential equation several times, and then eliminating certain quantities, say, by the use of resultants. We give the simplest example of this, that every C” solution of an ADE satisfi...
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The Grothendieck–Katz p-curvature conjecture predicts that an arithmetic differential equation whose reduction modulo p has vanishing pcurvatures for almost all p, has finite monodromy. It is known that it suffices to prove the conjecture for differential equations on P1−{0, 1,∞}. We prove a variant of this conjecture for P1−{0, 1,∞}, which asserts that if the equation satisfies a certain conve...
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SYSTEMS Yuan Wang Mathematics Department, Florida Atlantic University, Boca Raton, Fl 33431 (407)367-3317, E-mail: y [email protected] Eduardo D. Sontag Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 (908)932-3072, E-mail: [email protected] ABSTRACT An equivalence is shown between realizability of input/output operators by rational control systems and high orde...
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We prove that degrees of rational solutions of an algebraic differential equation F (dw/dz,w, z) = 0 are bounded. For given F an upper bound for degrees can be determined explicitly. This implies that one can find all rational solutions by solving algebraic equations. Consider the differential equation F (w′, w, z) = 0, (w′ = dw/dz) (1) where F is a polynomial in three variables. Theorem 1 For ...
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where F is a polynomial in the first k+ 1 variables, whose coefficients are analytic functions of the independent variable z. If the conditions of Cauchy's theorem for the existence and uniqueness of the solution are satisfied, then (0.1) determines an analytic function in a neighbourhood of a given point z0. One of the most difficult problems in the analytic theory of differential equations is...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1959
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1959-0107641-6