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Periodic Solutions to Painlevé VI and Dynamical System on Cubic Surface

Katsunori Iwasaki·Takato Uehara
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Abstract

The number of periodic solutions to Painlevé VI along a Pochhammer loop is counted exactly. It is shown that the number grows exponentially with period, where the growth rate is determined explicitly. Principal ingredients of the computation are a moduli-theoretical formulation of Painlevé VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.

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Katsunori Iwasaki, Takato Uehara. 2006-01-06. Periodic Solutions to Painlevé VI and Dynamical System on Cubic Surface. https://arxiv.org/abs/math/0512583

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