摘要翻译:
第六类Painleve方程在固定奇点附近的每一个有限分支解都是一个代数分支解。特别地,全局解是代数解当且仅当它是有限多值的全局解。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奇点的分解和代数微分方程的幂几何。在证明过程中,我们还能够将所有有限分支解分类到Backlund变换。
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英文标题:
《Finite branch solutions to Painleve VI around a fixed singular point》
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作者:
Katsunori Iwasaki
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Classical Analysis and ODEs 经典分析与颂歌
分类描述:Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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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.
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PDF链接:
https://arxiv.org/pdf/0704.0679