Painleve方程VI在固定奇点附近的有限分支解
Finite branch solutions to Painleve VI around a fixed singular point
摘要：
第六类Painleve方程围绕固定奇点的每一个有限分支解都是代数分支解。特别地，一个整体解是一个代数解当且仅当它是一个整体的多值解。这一结果的证明依赖于Painleve VI的代数几何、Riemann-Hilbert对应、三次曲面上的几何和动力学、Kleinian奇点的解析以及代数微分方程的幂几何。在过程中的证明，我们也能够分类的所有有限分支的解决方案，以Backlund变换。
英文摘要：
Every finite branch solutions to the sixth Painleve equation around a fixed singular point is an algebraic branch solution. In particular a global solution is an algebraic solution if and only if it is finitely many-valued globally. The proof of this result relies on algebraic geometry of Painleve VI, Riemann-Hilbert correspondence, geometry and dynamics on cubic surfaces, resolutions of Kleinian singularities, and power geometry of algebraic differential equations. In the course of the proof we are also able to classify all finite branch solutions up to Backlund transformations.
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。
