Configurations of critical points in complex polynomial differential equations

A. Gasull, M. J. Álvarez, R. Prohens

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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 languageEnglish
Pages (from-to)923-934
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
DOIs
Publication statusPublished - 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