Some applications of the EulerJacobi formula to differential equations
Authors:
Anna Cima, Armengol Gasull and Francesc Mañosas
Journal:
Proc. Amer. Math. Soc. 118 (1993), 151163
MSC:
Primary 58F21; Secondary 34C05
MathSciNet review:
1150647
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Abstract: The EulerJacobi 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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 A Cima and J. Llibre, Configurations of fans and nests of limit cycles for polynomial vector fields in the plane, J. Differential Equations 82 (1989), 7197. MR 1023302 (90m:58167)
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 Ye Yanqian and Ye Weiyin, A generalization of Berlinskii's theorem to cubic and quartic differential systems, preprint, 1988. MR 977808 (89m:34038)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199311506479
PII:
S 00029939(1993)11506479
Keywords:
Differential equation,
critical point,
Euler Jacobi formula,
center point
Article copyright:
© Copyright 1993
American Mathematical Society
