1 research outputs found
Polygons of Petrovic and Fine, algebraic ODEs, and contemporary mathematics
Here, 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 Petrovic on algebraic
differential equations and in particular his geometric ideas captured in his
polygon method from the last years of the XIXth century, which have been left
completely unnoticed by the experts. This concept, also developed in a bit a
different direction and independently by Henry Fine, generalizes the famous
Newton-Puiseux polygonal method and applies to algebraic ODEs rather than
algebraic equations. Although remarkable, the Petrovic legacy has been
practically neglected in the modern literature, while the situation is less
severe in the case of results of Fine. Thus, we study the development of the
ideas of Petrovic and Fine and their places in contemporary mathematics.Comment: 39 pages, 5 figure