Painleve equations, vector fields, and ranks in differential fields
Logic
2016-08-18 v1 Algebraic Geometry
Classical Analysis and ODEs
Abstract
Model theoretic ranks of solutions to Painleve equations are calculated, and the type of the generic solution of the second Painleve equation is shown to be disintegrated, strengthening a theorem of Nagloo. A question of Hrushovski and Scanlon regarding Lascar rank and Morley rank in differential fields is answered using planar vector fields.
Keywords
Cite
@article{arxiv.1608.04756,
title = {Painleve equations, vector fields, and ranks in differential fields},
author = {James Freitag},
journal= {arXiv preprint arXiv:1608.04756},
year = {2016}
}
Comments
7 pages