Some applications of the euler-jacobi formula to differential equations

Anna Cima; Armengol Gasull; Francesc MaÑosas

doi:10.1090/S0002-9939-1993-1150647-9

Some applications of the euler-jacobi formula to differential equations

Anna Cima, Armengol Gasull, Francesc MaÑosas

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

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. © 1993 American Mathematical Society.

Original language	English
Pages (from-to)	151-163
Journal	Proceedings of the American Mathematical Society
Volume	118
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1993-1150647-9
Publication status	Published - 1 Jan 1993

Keywords

Center point
Critical point
Differential equation
Euler Jacobi formula
Graph

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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. {\textcopyright} 1993 American Mathematical Society.",

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KW - Critical point

KW - Differential equation

KW - Euler Jacobi formula

KW - Graph

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