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Some applications of the Euler-Jacobi formula to differential equations

Authors: Anna Cima, Armengol Gasull and Francesc Mañosas
Journal: Proc. Amer. Math. Soc. 118 (1993), 151-163
MSC: Primary 58F21; Secondary 34C05
MathSciNet review: 1150647
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Abstract: The Euler-Jacobi formula gives an algebraic relation between the critical points of a vector field and their indices. Using this formula we obtain an upper bound for the number of centers that a planar polynomial differential equation can have and study the distribution of the critical points for planar quadratic and cubic differential equations.

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Keywords: Differential equation, critical point, Euler Jacobi formula, center point
Article copyright: © Copyright 1993 American Mathematical Society

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