On the Algebraic Independence of Generic Painlevé Transcendents
نویسندگان
چکیده
We prove that if y′′ = f(y, y′, t, α, β, . . .) is a generic Painlevé equation from among the classes II to V , and if y1, . . . , yn are distinct solutions, then tr.deg (C(t)(y1, y′ 1, . . . , yn, y′ n)/C(t)) = 2n. (This was proved by Nishioka for the single equation PI .) For generic Painlevé VI, we have a slightly weaker result: ω-categoricity (in the sense of model theory) of the solution space, as described below.
منابع مشابه
Painlevé transcendents in two-dimensional topological field theory
Introduction Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. Lecture 3. Semisimplicity and canonical coordinates. Lecture 4. Classification of semisimple Frobenius manifolds. Lecture 5. Mon...
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