Centers and Uniform Isochronous Centers of Planar Polynomial Differential Systems |
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Authors: | Jaume Llibre Rafael Ramírez Valentín Ramírez Natalia Sadovskaia |
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Affiliation: | 1.Departament de Matemàtiques,Universitat Autònoma de Barcelona,Barcelona,Spain;2.Departament d’Enginyeria Informàtica i Matemàtiques,Universitat Rovira i Virgili,Tarragona,Spain;3.Universitat de Barcelona,Barcelona,Spain;4.Departament de Matemàtica Aplicada II,Universitat Politècnica de Catalunya,Barcelona,Spain |
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Abstract: |
For planar polynomial vector fields of the form $$begin{aligned} (-y+X(x,y))dfrac{partial }{partial x}+(x+Y(x,y))dfrac{partial }{partial y}, end{aligned}$$ where X and Y start at least with terms of second order in the variables x and y, we determine necessary and sufficient conditions under which the origin is a center or a uniform isochronous centers. |
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