Geodesic
Equivalence of second-order ordinary differential equations to Painlev\'e equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 256-276

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All Painlevé equations except the first belong to one type of equations. In terms of invariants of these equations, we obtain criteria for the equivalence to the second Painlevé equation and to equation XXXIV in the list of $50$ equations without movable critical points. We find new necessary conditions of equivalence for the third and fourth and also special cases of the fifth and sixth Painlevé equations. We compare the invariants we use with invariants previously introduced by other authors and compare the obtained results.
Keywords: Painlevé equation
Mots-clés : equivalence, invariant. 
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     author = {Yu. Yu. Bagderina},
     title = {Equivalence of second-order ordinary differential equations to {Painlev\'e} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {256--276},
     publisher = {mathdoc},
     volume = {182},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a4/}
}
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Yu. Yu. Bagderina. Equivalence of second-order ordinary differential equations to Painlev\'e equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 182 (2015) no. 2, pp. 256-276. http://geodesic.mathdoc.fr/item/TMF_2015_182_2_a4/