Geodesic
Polynomial degree reduction of a~Fuchsian $2{\times}2$ system
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 223-230

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A Fuchsian $2{\times}2$ system generating the Painlevé equation $\mathrm P^6$ is acted on by a polynomial transformation similar to rotation in order to reduce the polynomial degree of matrices in the left- and the right-hand sides of the system. This clarifies the derivation of the Painlevé equation and the study of its symmetries.
Keywords: Fuchsian system, Painlevé equation. 
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     author = {S. Yu. Slavyanov},
     title = {Polynomial degree reduction of {a~Fuchsian} $2{\times}2$ system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {223--230},
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     number = {2},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a2/}
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S. Yu. Slavyanov. Polynomial degree reduction of a~Fuchsian $2{\times}2$ system. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 223-230. http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a2/