Quadratic systems with an integrable saddle: A complete classification in the coefficient space ℝ 12

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Abstract

A quadratic polynomial differential system can be identified with a single point of ℝ 12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of ℝ 12 having an integrable saddle. We show that there are only 47 topologically different phase portraits in the Poincaré disk associated to this family of quadratic systems up to a reversal of the sense of their orbits. Moreover each one of these 47 representatives is determined by a set of affine invariant conditions. © 2012 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)5416-5447
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number14
DOIs
Publication statusPublished - 1 Sep 2012

Keywords

  • Quadratic vector fields
  • Type of singularity
  • Weak saddle

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