@article{Dragovic:2020te,
    Abstract = {In 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 Petrovi{\'c}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 Petrovi{\'c}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 Petrovi{\'c}and Fine and their places in contemporary mathematics.},
    Author = {Dragovi{\'c}, Vladimir and Goryuchkina, Irina},
    Date = {2020/11/01},
    File = {Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics - Dragović-Goryuchkina2020\_Article\_PolygonsOfPetrovićAndFineAlgeb.pdf},
    ISBN = {1432-0657},
    Journal = {Archive for History of Exact Sciences},
    Number = {6},
    Pages = {523--564},
    Title = {Polygons of Petrovi{\'c} and Fine, algebraic ODEs, and contemporary mathematics},
    URL = {https://doi.org/10.1007/s00407-020-00250-3},
    Volume = {74},
    Year = {2020},
    bdsk-url-1 = {https://doi.org/10.1007/s00407-020-00250-3},
    date-added = {2022-04-30 22:52:40 +0200},
    date-modified = {2022-05-05 10:41:14 +0200},
    id = {Dragovi{\'c}2020},
    doi = {10.1007/s00407-020-00250-3}
}

@article{Dragovic:2020te, Abstract = {In 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 Petrovi{\'c}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 Petrovi{\'c}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 Petrovi{\'c}and Fine and their places in contemporary mathematics.}, Author = {Dragovi{\'c}, Vladimir and Goryuchkina, Irina}, Date = {2020/11/01}, File = {Polygons of Petrović and Fine, algebraic ODEs, and contemporary mathematics - Dragović-Goryuchkina2020_Article_PolygonsOfPetrovićAndFineAlgeb.pdf}, ISBN = {1432-0657}, Journal = {Archive for History of Exact Sciences}, Number = {6}, Pages = {523--564}, Title = {Polygons of Petrovi{\'c} and Fine, algebraic ODEs, and contemporary mathematics}, URL = {https://doi.org/10.1007/s00407-020-00250-3}, Volume = {74}, Year = {2020}, bdsk-url-1 = {https://doi.org/10.1007/s00407-020-00250-3}, date-added = {2022-04-30 22:52:40 +0200}, date-modified = {2022-05-05 10:41:14 +0200}, id = {Dragovi{\'c}2020}, doi = {10.1007/s00407-020-00250-3} }