Six results on Painleve VI
Algebraic Geometry
2007-05-23 v3 Classical Analysis and ODEs
Exactly Solvable and Integrable Systems
Abstract
After recalling some of the geometry of the sixth Painleve equation, we will describe how the Okamoto symmetries arise naturally from symmetries of Schlesinger's equations and summarise the classification of the Platonic Painleve six solutions. A key observation is that Painleve VI governs the isomonodromic deformations of certain Fuchsian systems on rank \emph{three} bundles.
Keywords
Cite
@article{arxiv.math/0503043,
title = {Six results on Painleve VI},
author = {Philip Boalch},
journal= {arXiv preprint arXiv:math/0503043},
year = {2007}
}
Comments
16 pages, written for Angers 2004 International Conference on Asymptotic Theories and Painleve Equations (updated, added Remark 7 giving simple formulae for isomonodromic families of rank three systems in terms of PVI solutions and as an example the full family of "Klein connections" are written down)