Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four

Joan C. Artés, Jaume Llibreb, Dana Schlomiuk, Nicolae Vulpe

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1 Citation (Scopus)

Abstract

© 2015, University of Szeged. All Rights Reserved. In this article we obtain the geometric classification of singularities, finite and infinite, for the two subclasses of quadratic differential systems with total finite multiplicity m<inf>f</inf> = 4 possessing exactly three finite singularities, namely: systems with one double real and two complex simple singularities (31 configurations) and (ii) systems with one double real and two simple real singularities (265 configurations). We also give here the global bifurcation diagrams of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for these classes of quadratic systems. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants. This gives an algorithm for determining the geometric configuration of singularities for any system in anyone of the two subclasses considered.
Original languageEnglish
Article number49
JournalElectronic Journal of Qualitative Theory of Differential Equations
Volume2015
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Affine invariant polynomials
  • Configuration of singularities
  • Geometric equivalence relation
  • Infinite and finite singularities
  • Poincaré compactification
  • Quadratic vector fields

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