简化具有一般系数的矩阵微分方程

IF 0.8 2区数学 Q2 MATHEMATICS

Israel Journal of Mathematics Pub Date : 2023-12-18 DOI:10.1007/s11856-023-2599-0

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引用次数: 0

摘要

摘要我们证明了具有 n2 个一般系数的 n × n 矩阵微分方程 δ(Y) = AY 无法通过使用其系数为 A 的矩阵项中的有理函数及其导数的规整变换简化为小于 n 个参数的方程。我们的证明使用了微分伽罗瓦理论和本质维度的微分类似方法。我们还限定了描述某些一般皮卡-维西奥扩展所需的最小参数数。

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Simplifying matrix differential equations with general coefficients

Abstract

We show that the n × n matrix differential equation δ(Y) = AY with n² general coefficients cannot be simplified to an equation in less than n parameters by using gauge transformations whose coefficients are rational functions in the matrix entries of A and their derivatives. Our proof uses differential Galois theory and a differential analogue of essential dimension. We also bound the minimum number of parameters needed to describe some generic Picard–Vessiot extensions.

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来源期刊

Israel Journal of Mathematics 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

审稿时长

6 months

期刊介绍： The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.