Journal of the Mathematical Society of Japan

On an orbifold Hamiltonian structure for the first Painlevé equation

Katsunori IWASAKI and Shu OKADA

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For the first Painlevé equation we establish an orbifold polynomial Hamiltonian structure on the fibration of Okamoto's spaces and show that this geometric structure uniquely recovers the original Painlevé equation, thereby solving a problem posed by K. Takano.

Article information

J. Math. Soc. Japan Volume 68, Number 3 (2016), 961-974.

First available in Project Euclid: 19 July 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 33E17: Painlevé-type functions
Secondary: 34M55: Painlevé and other special equations; classification, hierarchies;

the first Painlevé equation Hamiltonian system orbifold


IWASAKI, Katsunori; OKADA, Shu. On an orbifold Hamiltonian structure for the first Painlevé equation. J. Math. Soc. Japan 68 (2016), no. 3, 961--974. doi:10.2969/jmsj/06830961.

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