On the Algebraic Solutions of the Painlev\'e-III (D$_7$) Equation

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• Peter Miller (University of Michigan)
• Tuesday 11 October 2022, 15:00-17:00
• Seminar Room 2, Newton Institute.

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ARA2 - Applicable resurgent asymptotics: towards a universal theory

The D$_7$ degeneration of the Painlev\’e-III equation has, for certain integral parameter values, a unique algebraic solution that is a rational function of the cube root of the independent variable.  This talk will describe some properties of these solutions, develop a Riemann-Hilbert representation of them using the isomonodromy method, and explain how asymptotic properties of the solutions, including an approximation by Weierstra\ss\ elliptic functions, are obtained from that representation.  This is joint work with Robert Buckingham.

This talk is part of the Isaac Newton Institute Seminar Series series.

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