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Necessary Conditions for Point Equivalence of Second-Order Odes to the Sixth Painlevé Equation

We consider the equivalence problem for projective-type scalar second-order ordinary differential equations with respect to invertible point changes of variables. Invariants of the equivalence transformation group of this family of equations are used to find necessary conditions for equivalence to the sixth Painlevé equation.

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Correspondence to Yu. Yu. Bagderina.

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Dedicated to M. A. Semenov–Tian-Shansky on the occasion of his 70th birthday

Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 473, 2018, pp. 17–33.

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Bagderina, Y.Y. Necessary Conditions for Point Equivalence of Second-Order Odes to the Sixth Painlevé Equation. J Math Sci 242, 595–607 (2019). https://doi.org/10.1007/s10958-019-04499-0

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  • DOI: https://doi.org/10.1007/s10958-019-04499-0