On singularities of certain non-linear second-order ordinary differential equations
The authors use the method of blowing up points of indeterminacy of certain systems of two ordinary differential equations in order to analyse the singularity structure of the solutions of the corresponding non-linear differential equations. They deal with the Painlevé example in which they explain the structure of singularities of the original equation. In the context of the Painlevé test they apply regularising of bi-rational transformations. They consider Smith's example with non-isolated singularity in which the sequence of blow-ups can be infinite. They treat also the Painlevé-Ince equation in which both positive and negative resonances occur.
scientific article; zbMATH DE number 7464304
scientific article