Circular pentagons and real solutions of Painleve VI equations
Complex Variables
2018-01-23 v1 Mathematical Physics
math.MP
Abstract
We study real solutions of a class of Painleve VI equations. To each such solution we associate a geometric object, a one-parametric family of circular pentagons. We describe an algorithm which permits to compute the numbers of zeros, poles, 1-points and fixed points of the solution on the interval x>1 and their mutual position. The monodromy of the associated linear equation and parameters of the Painleve VI equation are easily recovered from the family of pentagons.
Cite
@article{arxiv.1611.01356,
title = {Circular pentagons and real solutions of Painleve VI equations},
author = {Alexandre Eremenko and Andrei Gabrielov},
journal= {arXiv preprint arXiv:1611.01356},
year = {2018}
}
Comments
55 pages, 24 figures