Rational Solutions of the Painleve' VI Equation

Abstract

In this paper, we classify all values of the parameters $\alpha$, $\beta$, $\gamma$ and $\delta$ of the Painlevé VI equation such that there are rational solutions. We give a formula for them up to the birational canonical transformations and the symmetries of the Painlevé VI equation.

13 pages, 1 Postscript figure Typos fixed

Cited by in corpus (15)

• Matching Procedure for the Sixth Painlevé Equation (May 2006)
• A Review on The Sixth Painleve' Equation
• Tabulation of PVI Transcendents and Parametrization Formulas (August 17, 2011)
• New contiguity relation of the sixth Painlevé equation from a truncation
• A Riemann-Hilbert Approach to the Heun Equation
• Poles Distribution of PVI Transcendents close to a Critical Point (summer 2011)
• Rational solutions of the Noumi and Yamada system of type $A_4^{(1)}$
• Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
• Apparent singularities of Fuchsian equations, and the Painlevé VI equation and Garnier systems
• Wronskian Appell Polynomials and Symmetric Functions
• Determinant formulas for the five-vertex model
• Classification of algebraic solutions of irregular Garnier systems
• Rational Solutions of the Sasano System of Type $A_5^{(2)}$
• Rational solutions of the Sasano system of type $D_5^{(1)}$
• Singular Instantons and Painlevé VI