Geodesic
The discrete and continuous Painlevé VI hierarchy and the Garnier systems
Glasgow mathematical journal, Tome 43 (2001) no. A, pp. 109-123

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We present a general scheme to derive higher-order members of the Painlevé VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits on the background of the PVI equation and that consists of a system of partial difference equations on a multidimensional lattice. The connection with the isomonodromic Garnier systems is discussed. 
Nijhoff, F. W.; Walker, A. J. The discrete and continuous Painlevé VI hierarchy and the Garnier systems. Glasgow mathematical journal, Tome 43 (2001) no. A, pp. 109-123. doi: 10.1017/S0017089501000106
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     title = {The discrete and continuous {Painlev\'e} {VI} hierarchy and the {Garnier} systems},
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