Electron. J. Diff. Equ., Vol. 2012 (2012), No. 09, pp. 1-35.

Complete geometric invariant study of two classes of quadratic systems

Joan C. Artes, Jaume Llibre, Nicolae Vulpe

Abstract:
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 [30] that studied centers up to GL-invariant, and over the results in [1] 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.

Submitted May 16, 2011. Published January 13, 2012.
Math Subject Classifications: 34C05, 34A34.
Key Words: Quadratic vector fields; weak singularities; type of singularity.

Show me the PDF file (530 KB), TEX file, and other files for this article.

Joan C. Artés
Departament de Matemátiques
Universitat Autónoma de Barcelona
08193 Bellaterra, Barcelona, Spain
email: artes@mat.uab.cat
Jaume Llibre
Departament de Matemátiques
Universitat Autónoma de Barcelona
08193 Bellaterra, Barcelona, Spain
email: jllibre@mat.uab.cat
Nicolae Vulpe
Institute of Mathematics and Computer Science
Academy of Science of Moldova
5 Academiei str, Chisinau, MD-2028, Moldova
email: nvulpe@gmail.com

Return to the EJDE web page