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