三次曲面上Painlevé VI与动力系统的周期解
Periodic Solutions to Painlevé VI and Dynamical System on Cubic Surface
摘要：
Painlevé VI沿着Pochhammer环的周期解的数目被精确地计数。结果表明，该数字随时间呈指数增长，其中的增长率是明确确定的。计算的主要成分是Painlevé VI的模理论公式、Riemann-Hilbert对应、三次曲面上双有理映射的动力系统和Lefschetz不动点公式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
