奇异三次曲面与Painleve VI动力学
Singular cubic surfaces and the dynamics of Painleve VI
摘要：
我们开发了一个动力学研究的第六Painleve方程的所有参数概括了较早的工作通用参数。本文的主要研究对象是非类属参数，其对应的特征变量是具有简单奇异性的三次曲面，Riemann-Hilbert对应是奇异曲面的最小分解，而不是类属情况下的双全纯.在参数空间上引入适当的分层，基于奇异三次曲面的几何性质，建立了Painleve VI非线性单值映射的混沌性质，并给出了其孤立周期解个数的精确估计.
英文摘要：
We develop a dynamical study of the sixth Painleve equation for all parameters generalizing an earlier work for generic parameters. Here the main focus of this paper is on non-generic parameters, for which the corresponding character variety becomes a cubic surface with simple singularities and the Riemann-Hilbert correspondence is a minimal resolution of the singular surface, not a biholomorphism as in the generic case. Introducing a suitable stratification on the parameter space and based on geometry of singular cubic surfaces, we establish a chaotic nature of the nonlinear monodromy map of Painleve VI and give a precise estimate for the number of its isolated periodic solutions.
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