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

DOI:
https://doi.org/10.1090/S0002-9939-1993-1150647-9

MathSciNet review:
1150647

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1993-1150647-9

Keywords:
Differential equation,
critical point,
Euler Jacobi formula,
center point

Article copyright:
© Copyright 1993
American Mathematical Society