Family of quadratic differential systems with invariant hyperbolas: a complete classification in the space R12
Oliveira, Regilene (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação)
Rezende, Alex C. (Universidade de São Paulo. Instituto De Ciências Matemáticas e de Computação)
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)

Date:	2016
Abstract:	In this article we consider the class QS of all non-degenerate quadratic systems. A quadratic polynomial differential system can be identified with a single point of R12 through its coefficients. In this paper using the algebraic invariant theory we provided necessary and sufficient conditions for a system in QS to have at least one invariant hyperbola in terms of its coefficients. We also considered the number and multiplicity of such hyperbolas. We give here the global bifurcation diagram of the class QS of systems with invariant hyperbolas. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants. The results can therefore be applied for any family of quadratic systems in this class, given in any normal form.
Grants:	European Commission 316338
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Affine invariant polynomials ; Group action ; Invariant hyperbola ; Quadratic differential systems
Published in:	Electronic journal of differential equations, Vol. 2016, Issue 162 (2016) , p. 1-50, ISSN 1072-6691

Adreça alternativa: https://ejde.math.txstate.edu/Volumes/2016/162/oliveira.pdf

Postprint 53 p, 809.9 KB

50 p, 719.2 KB

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