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The geometry of some tridimensional families of planar quadratic differential systems
Rezende, Alex C. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Artés, Joan Carles, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Publicació: [São Paolo] Universidade de São Paolo 2014
Descripció: 1 recurs electrònic (342 p.)
Resum: Planar quadratic differential systems occur in many areas of applied mathematics. Although more than one thousand papers have been written on these systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert's 16th problem, are still open for this family. One of the goals of recent researchers is the topological classification of quadratic systems. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a large number), many subclasses are considered and studied. Specific characteristics are taken into account and this implies a decrease in the number of parameters, which makes possible the study. In this thesis we mainly study two subfamilies of quadratic systems: the first one possessing a finite semi-elemental triple node and the second one possessing a finite semi-elemental-saddle-node and an infinite semi-elemental saddle-node formed by the collision of an infinite saddle with an infinite node. The bifurcation diagram for both families ae tridimensional. The family having the triple node yields 28 topologically distinct phase portraits, whereas the closure of the family having the saddle-nodes within the bifurcation sets and the phase portraits are represented on the Poincaré disk. The bifurcation sets are the union of algebraic surfaces and surfaces whose presence was detected numerically. Moreover, we also present the analysis of a differential system known as SIS model (this kind of systems are esasily found in applied mathematics) and the complete classification of quadratic systems possessing invariant hyperbolas.
Nota: Tesi doctoral - Universidade de Sao Paulo. Instituto de Ciências Matemáticas e de Computaçao, 2014.
Drets: L'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons Creative Commons
Llengua: Anglès
Document: doctoralThesis ; recerca
Matèria: Quadratic differential systems ; Topological classification ; Affine invariant polynomials ; Semi–elemental triple node ; Semi–elemental saddle–node ; Global phase portrait ; SIS model ; Invariant hyperbola

372 p, 4.1 MB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
Documents de recerca > Tesis doctorals

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