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On generalized Sundman transformation method, first integrals, symmetries and solutions of equations of Painlevé-Gambier type. (English) Zbl 1193.34074
The authors introduce the notion of a generalized Sundman transformation and define the associated Sundman symmetry for second order ODEs of the Painlevé-Gambier classification with the aim to compute new first integrals of Jacoi and special cases of Jacobi equations as particular equations of the Painlevé-Gambier classification. Sundman transformation allows to construct parametric solutions of these equations.

34C14Symmetries, invariants (ODE)
34C20Transformation and reduction of ODE and systems, normal forms
34A05Methods of solution of ODE
Full Text: DOI
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