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- ItemClassification of the family of quadratic differential systems possessing invariant ellipses.(2019-04) Oliveira, Regilene Delazari dos Santos; Rezende, Alex C.; Schlomiuk, Dana; Vulpe, Nicolae
Mostrar mais Consider the class QS of all non-degenerate quadratic systems. Note that each quadratic polynomial differential system can be identiffed with a point of R12 through its coeffcients. In this paper we provide necessary and suffcient conditions for a system in QS, in term of its coeffcients, to have at least one invariant ellipse. Let QSE be the whole class of non-degenerate planar quadratic differential systems possessing at least one invariant ellipse. For the class QSE, we give the global \bifurcation" diagram which indicates where an ellipse is present or absent and in case it is present, the diagram indicates if the ellipse is or not a limit cycle. The diagram is expressed in terms of affne invariant polynomials and it is done in the 12-dimensional space of parameters. This diagram is also an algorithm for determining for each quadratic system if it possesses an invariant ellipse and whether or not this ellipse is a limit cycle.Mostrar mais - ItemFamily of quadratic differential systems with irreducible invariant hyperbolas: a complete classification in the space R 12.(2014) Oliveira, Regilene Delazari dos Santos; Rezende, Alex C.; Vulpe, Nicolae
Mostrar mais In this article we consider the class QSf of all quadratic systems possessing a finite number of singularities (finite and infinite).Mostrar mais - ItemGeometric analysis of quadratic differential systems with invariant ellipses.(2019-10) Mota, Marcos C.; Oliveira, Regilene Delazari dos Santos; Rezende, Alex C.; Schlomiuk, Dana; Vulpe, Nicolae
Mostrar mais n this article we study the whole class QSE of non-degenerate planar quadratic differential systems possessing at least one invariant ellipse.We classify this family of systems according to their geometric properties encoded in the configurations of invariant ellipses and invariant straight lines which these systems could possess. The classification, which staken modulo the action of t he group of real affine transformations and time rescaling, is given in terms of algebraic geometric invariants and also in terms of invariant polynomials and it yields a total of 35 distinct such configurations. This classification is also an algorithm which makes it possible to verify for any given real quadratic differential system if it has invariant ellipses or not and to specify its configuration of invariant ellipses and straight lines.Mostrar mais