On singularities of certain non-linear second-order ordinary differential equations
type: Item
instance of: scholarly article
title: On singularities of certain non-linear second-order ordinary differential equations
zbMATH Open document ID: 1490.34113
author: Galina Filipuk
author: Thomas Kecker
published in: Results in Mathematics
publication date: 2022-01-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 14E15
zbMATH DE Number: 7464304
zbMATH Keywords: blowing up of singularities
zbMATH Keywords: Painlevé-Ince equation
zbMATH Keywords: Painlevé test
reviewed by: Vladimir P. Kostov
MaRDI profile type: Publication
full work available at URL: s00025-021-01577-1
OpenAlex ID: W4200452255
Wikidata QID: Q115389817
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DOI: 10.1007/S00025-021-01577-1
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description: scientific article; zbMATH DE number 7464304