Periodic Solutions to Painlevé VI and Dynamical System on Cubic Surface

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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.
26 pages, 10 figures, 4 tables

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Algebraic Geometry, Dynamical Systems, 34M55; 37F10

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http://salesiana.dossiersoluciones.com/handle/123456789/106393

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512583
 http://arxiv.org/abs/math/0512583

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arXiv