Exceptional solutions to the Painlev\'e VI equation
Alexandre Eremenko, Andrei Gabrielov, Aimo Hinkkanen
TL;DR
This paper classifies special solutions to the Painlevé VI equation that are free of zeros, poles, 1-points, and fixed points, providing a complete characterization of these exceptional solutions.
Contribution
It identifies all solutions of Painlevé VI lacking zeros, poles, 1-points, and fixed points, which was previously unknown.
Findings
All such solutions are explicitly characterized.
The solutions exhibit unique properties avoiding common singularities.
This classification advances understanding of Painlevé VI special solutions.
Abstract
We find all solutions of the Painlev\'e VI equations with the property that they have no zeros, no poles, no 1-points and no fixed points.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.