Complete geometric invariant study of two classes of quadratic systems

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In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in that studied centers up to GL-invariant, and over the results in that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite. © 2012 Texas State University - San Marcos.
Original languageEnglish
Pages (from-to)1-35
JournalElectronic Journal of Differential Equations
Publication statusPublished - 31 Jan 2012


  • Quadratic vector fields
  • Type of singularity
  • Weak singularities


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