Phase portraits of the quadratic vector fields with a polynomial first integral |
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| Authors: | Belén García Jesús S Pérez Del Río Jaume Llibre |
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| Institution: | 1. Departamento de Matemáticas, Universidad de Oviedo, Avda Calvo Sotelo s/n, 33007, Oviedo, Spain
2. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Barcelona, Spain
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| Abstract: | In this work we classify the phase portraits of all quadratic polynomial differential systems having a polynomial first integral.
IfH(x, y) is a polynomial of degreen+1 then the differential systemx′=−∂H/∂y,y′=∂H/∂x is called a Hamiltonian system of degreen. We also prove that all the phase portraits that we obtain in this paper are realizable by Hamiltonian systems of degree
2. |
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