MR2177121 Sakai, Hidetaka Hidetaka SAKAI A $q$-Analog of the Garnier System Funkcialaj Ekvacioj. Serio Internacia 48 2005 273--297 http://fe.math.kobe-u.ac.jp/FE/FullPapers/48-2/48_273.pdf http://www.ams.org/mathscinet-getitem?mr=MR2177121 A $q$-difference analog of the Garnier system is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit is also studied. Integrable system, $q$-Difference equation, Painlevé equations, Garnier system. 33E17, 34M55, 39A12, 39A13. 48-273 2005 A $q$-Analog of the Garnier System SAKAI, Hidetaka Hidetaka SAKAI
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