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28 p, 571.0 KB

Complete geometric invariant study of two classes of quadratic systems / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
In this paper we give a complete study using affine invariant conditions for the quadratic systems having centers. Independently we do the same for quadratic systems being Hamiltonian. There are two improvements of the previous results as [29] in which centers where study up to GL-invariant, and of [1] in which Hamiltonian QS where classified without invariants. [...]
2012
Electronic journal of differential equations, Vol. 2012 Núm. 9 (2012) , p. 1-35

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38 p, 831.0 KB

Quadratic systems with an integrable saddle: A complete classification in the coefficient space R^12 / Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
A quadratic polynomial differential system can be identified with a single point of R12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of R12 having an integrable saddle. [...]
2012 - DOI (Digital Object Identifier)

10.1016/j.na.2012.04.043
Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 5416-5447

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