On the reduction of the degree of linear differential operators
Classical Analysis and ODEs
2015-05-18 v1 Dynamical Systems
Abstract
Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type.
Keywords
Cite
@article{arxiv.1003.0629,
title = {On the reduction of the degree of linear differential operators},
author = {Marcin Bobieński and Lubomir Gavrilov},
journal= {arXiv preprint arXiv:1003.0629},
year = {2015}
}