Periodic Solutions to Painlev\'e VI and Dynamical System on Cubic Surface
代数几何
2007-05-23 v3 动力系统
摘要
The number of periodic solutions to Painlev\'e 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 Painlev\'e VI, a Riemann-Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula.
引用
@article{arxiv.math/0512583,
title = {Periodic Solutions to Painlev\'e VI and Dynamical System on Cubic Surface},
author = {Katsunori Iwasaki and Takato Uehara},
journal= {arXiv preprint arXiv:math/0512583},
year = {2007}
}
备注
26 pages, 10 figures, 4 tables