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dc.contributor.authorDragović, Vladimiren_US
dc.contributor.authorGoryuchkina, Irinaen_US
dc.date.accessioned2020-07-11T07:16:43Z-
dc.date.available2020-07-11T07:16:43Z-
dc.date.issued2020-01-01-
dc.identifier.issn0003-9519-
dc.description.abstractIn this paper, we study the genesis and evolution of geometric ideas and techniques in investigations of movable singularities of algebraic ordinary differential equations. This leads us to the work of Mihailo Petrović on algebraic differential equations (ODEs) and in particular the geometric ideas expressed in his polygon method from the final years of the nineteenth century, which have been left completely unnoticed by the experts. This concept, also developed independently and in a somewhat different direction by Henry Fine, generalizes the famous Newton–Puiseux polygonal method and applies to algebraic ODEs rather than algebraic equations. Although remarkable, the Petrović legacy has been practically neglected in the modern literature, although the situation is less severe in the case of results of Fine. Therefore, we study the development of the ideas of Petrović and Fine and their places in contemporary mathematics.en_US
dc.publisherSpringer Linken_US
dc.relationGeometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systemsen_US
dc.relationGrant PRAS-18-01 (PRAN 01 “Fundamental mathematics and its applications”)en_US
dc.relation.ispartofArchive for History of Exact Sciencesen_US
dc.titlePolygons of Petrović and Fine, algebraic ODEs, and contemporary mathematicsen_US
dc.typeArticleen_US
dc.identifier.doi10.1007/s00407-020-00250-3-
dc.identifier.scopus2-s2.0-85087134929-
dc.contributor.affiliationMathematical Institute of the Serbian Academy of Sciences and Artsen_US
dc.relation.grantno174020en_US
dc.description.rankM22-
item.grantfulltextnone-
item.cerifentitytypePublications-
item.fulltextNo Fulltext-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.openairetypeArticle-
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