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The qualitative theory of differential equations in the plane. (English) Zbl 1088.01012

Bolibruch, A.A. (ed.) et al., Mathematical events of the twentieth century. Transl. from the Russian. Berlin: Springer; Moscow: PHASIS (ISBN 3-540-23235-4/hbk). 101-132 (2006).
A survey of the development of the qualitative theory of differential equations from the point of view of its connections with the second (unsolved) part of Hilbert’s 16th problem (“What can be said about the number and location of limit cycles of a polynomial vector field of degree \(n\) on the plain?”)
For the entire collection see [Zbl 1072.01002].

MSC:

01A60 History of mathematics in the 20th century
34-03 History of ordinary differential equations
34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
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