Configurations of critical points in complex polynomial differential equations

A. Gasull; M. J. Álvarez; R. Prohens

doi:https://doi.org/10.1016/j.na.2008.11.018

Configurations of critical points in complex polynomial differential equations

A. Gasull, M. J. Álvarez, R. Prohens

Department of Mathematics

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

6 Citations (Scopus)

Abstract

In this work we focus on the configuration (location and stability) of simple critical points of polynomial differential equations of the form over(z, ̇) = f (z), z ∈ C. The case where all the critical points are of center type is studied in more detail finding several new center configurations. One of the main tools in our approach is the 1-dimensional Euler-Jacobi formula. © 2008 Elsevier Ltd. All rights reserved.

Original language	English
Pages (from-to)	923-934
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	71
DOIs	https://doi.org/10.1016/j.na.2008.11.018
Publication status	Published - 1 Aug 2009

Keywords

Center type critical points
Configuration of singularities
Euler-Jacobi formula
Holomorphic vector field
Polynomial vector field

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Gasull, A., Álvarez, M. J., & Prohens, R. (2009). Configurations of critical points in complex polynomial differential equations. Nonlinear Analysis, Theory, Methods and Applications, 71, 923-934. https://doi.org/10.1016/j.na.2008.11.018

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KW - Configuration of singularities

KW - Euler-Jacobi formula

KW - Holomorphic vector field

KW - Polynomial vector field

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