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Dynamics of the Sixth Painlev\'e Equation

Michi-aki Inaba·Katsunori Iwasaki·Masa-Hiko Saito
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Abstract

The sixth Painlev\'e equation is hiding extremely rich geometric structures behind its outward appearance. This article tries to give as a total picture as possible of its dynamical natures, based on the Riemann-Hilbert approach recently developed by the authors, using various techniques from algebraic geometry. A good part of the contents is extended to Garnier systems, while this article is restricted to the original sixth Painlev\'e equation.

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Michi-aki Inaba, Katsunori Iwasaki, Masa-Hiko Saito. 2005-01-01. Dynamics of the Sixth Painlev\'e Equation. https://arxiv.org/abs/math/0501007

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