Hierarchy of B\"acklund Transformation Groups of the Painlev\'e Systems
Classical Analysis and ODEs
2012-02-02 v1
Abstract
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.
Cite
@article{arxiv.math/0405559,
title = {Hierarchy of B\"acklund Transformation Groups of the Painlev\'e Systems},
author = {Masaki Suzuki and Nobuhiko Tahara and Kyoichi Takano},
journal= {arXiv preprint arXiv:math/0405559},
year = {2012}
}
Comments
11 pages, to be published in J. Math. Soc. Japan