A. M. Tresse, “Détermination des Invariants Ponctuels de l'équation Différentielle Ordinaire du Second Ordre y''=ω(x,y,y'),” Preisschriften der Furstlichen Jablonowski’schen Gesellschaft XXXII, Leipzig, 1896.

has been cited by the following article:

• TITLE: Equivalence Problem of the Painlevé Equations

  AUTHORS: Sopita Khamrod

  KEYWORDS: Equivalence Problem; Painlevé Equations; Point Transformation

  JOURNAL NAME: Advances in Pure Mathematics, Vol.3 No.2, March 19, 2013

  ABSTRACT: The manuscript is devoted to the equivalence problem of the Painlevé equations. Conditions which are necessary and sufficient for second-order ordinary differential equations y″=F (x ,y, y′) to be equivalent to the first and second Painlevé equation under a general point transformation are obtained. A procedure to check these conditions is found.