Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

Details Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems Hierarchy of Bäcklund Transformation Groups of the Painlevé Systems

2004-05-28

arxiv.org/abs/math/0405559v1

J. Math. Soc. Japan, Volume 56, Number 4 (2004), 1221-1232

Mathematics

Classical Analysis and ODEs

11 pages, to be published in J. Math. Soc. Japan

Scientific paper

10.2969/jmsj/1190905457

For each Painlev\'e system P_J except the first one, we have a B\"acklund
transformation group which is a lift of an affine Weyl group. In this paper, we
show that the B\"acklund transformation groups for J=V,IV,III,II are
successively obtained from that for J=VI by the well known degeneration or
confluence processes.

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