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Note on a theorem of Berlinskiĭ

Author: Andrés Sestier
Journal: Proc. Amer. Math. Soc. 78 (1980), 358-360
MSC: Primary 34C05
MathSciNet review: 553376
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Abstract: If a quadratic differential system has four singular points, these are elementary and the sum of their indices is 0 iff the quadrilateral with vertices at the singular points is convex; otherwise the sum of indices is 2 or $ - 2$. These facts and the relative positions of the two kinds of singular points are readily proved by consideration of the pencil of isoclines of the system. The theorem is originally due to Berlinskii.

References [Enhancements On Off] (What's this?)

  • [1] W. A. Coppel, A survey of quadratic systems, J. Differential Equations 2 (1966), 293-304. MR 0196182 (33:4374)
  • [2] Plaat, Ordinary differential equations, Holden-Day, San Francisco, Calif., 1971.

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Article copyright: © Copyright 1980 American Mathematical Society

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