Centennial History of Hilbert’s 16th Problem

  title={Centennial History of Hilbert’s 16th Problem},
  author={Yulii Il'yashenko},
  journal={Bulletin of the American Mathematical Society},
  • Y. Il'yashenko
  • Published 2002
  • Mathematics
  • Bulletin of the American Mathematical Society
The second part of Hilbert’s 16th problem deals with polynomial differential equations in the plane. It remains unsolved even for quadratic polynomials. There were several attempts to solve it that failed. Yet the problem inspired significant progress in the geometric theory of planar differential equations, as well as bifurcation theory, normal forms, foliations and some topics in algebraic geometry. The dramatic history of the problem, as well as related developments, are presented below. §1… Expand

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