Internality of logarithmic-differential pullbacks
Logic
2019-11-11 v2
Abstract
A criterion in the spirit of Rosenlicht is given, on the rational function f(x), for when the planar vector field defined by x'=f(x) and y'=xy admits a pair of algebraically independent first integrals over some extension of the base field. This proceeds from model-theoretic considerations by working in the theory of differentially closed fields of characteristic zero and asking: If D is a strongly minimal set on the affine line that is internal to the constants, when is the pullback of D under the logarithmic derivative itself internal to the constants?
Cite
@article{arxiv.1906.08659,
title = {Internality of logarithmic-differential pullbacks},
author = {Ruizhang Jin and Rahim Moosa},
journal= {arXiv preprint arXiv:1906.08659},
year = {2019}
}
Comments
26 pages