Rational Surfaces Associated with Affine Root Systems¶and Geometry of the Painlevé Equations

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書誌事項

公開日
2001-06-01
権利情報
  • http://www.springer.com/tdm
DOI
  • 10.1007/s002200100446
公開者
Springer Science and Business Media LLC

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説明

Here, the author provides an understanding of (discrete and continuous) Painlevé equations from a purely geometric point of view. The paper is motivated by previous work of Okamoto (and later Takano), but turns this work on its head by beginning with geometric structures and then deriving equations, along with many of their important properties. Thus, in addition to Painlevé equations, this geometric framework is also shown to yield Bäcklund transformations, special integrals and elliptic function limits. The author also gives a generic discrete equation which contains all other discrete equations which appear in the paper.

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