Simplifying matrix differential equations with general coefficients.

Autor: Tsui, Man Cheung
Zdroj: Israel Journal of Mathematics; May2024, Vol. 261 Issue 1, p473-491, 19p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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